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Practice: algebraic expressions, like terms and the distributive law

Algebra, grade 7 Lesson 15 of 22Practice

Practice: algebraic expressions, like terms and the distributive law

1

Write an algebraic expression: a. the number 6 times as large as n\displaystyle n; b. the number 4 less than the opposite of n\displaystyle n; c. the price of k\displaystyle k kg of apples, if one kg costs 8 ₪; d. the number of wheels on a\displaystyle a cars and b\displaystyle b bicycles.

2

Find the value of each expression.
Start with the substitution.
a. 7−3x\displaystyle 7-3x for x=−2\displaystyle {x}={-2}; b. a2−4a\displaystyle a^2-4a for a=−1\displaystyle {a}={-1}; c. xy+y\displaystyle xy+y for x=−3\displaystyle {x}={-3} and y=5\displaystyle {y}={5}.

a

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

    b

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

      c

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

        3

        Collect like terms.

        a

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

          b

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

            c

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

              4

              Open the brackets.

              a

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                b

                  / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                  / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                  c

                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                    d

                      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                      5

                      Simplify.

                      a

                        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                        b

                          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                          c

                            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                            6

                            Which of the equalities are identities?
                            For each one that is not, give a counterexample.
                            a. 3(x+1)=3x+1\displaystyle {3(x+1)}={3x+1}; b. 5−(x−2)=7−x\displaystyle {5-(x-2)}={7-x}; c. 2x+3x=5x2\displaystyle {2x+3x}={5x^2}; d. −(a+b)=−a−b\displaystyle {-(a+b)}={-a-b}.

                            7

                            We build a row of hexagons out of matches, each hexagon sharing a side with the one before: one hexagon takes 6 matches, two hexagons take 11, and three hexagons take 16.
                            Draw the fourth stage.
                            Write an expression for the number of matches in n\displaystyle n hexagons, and work out how many matches 50 hexagons take.

                            50 hexagons

                              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                              8

                              A rectangle is 2x\displaystyle 2x long and x+3\displaystyle x+3 wide.
                              Write an expression for its perimeter and simplify it.

                              9

                              Yael simplified like this: 5−2(x−4)=5−2x−8=−3−2x\displaystyle {5-2(x-4)}={5-2x-8}={-3-2x}.
                              Where is the mistake?
                              Simplify correctly.

                                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                                10

                                Simplify the expression 4(x−2)−3(x−5)\displaystyle 4(x-2)-3(x-5), then find its value for x=−6\displaystyle {x}={-6} – it is easier in the simplified expression.

                                  / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                                  / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power