Practice: inequalities

Algebra, grade 8 Lesson 26 of 27Practice

Practice: inequalities

Each axis shows the solution set of an inequality.
Write the inequality.

\displaystyle ?

\displaystyle ?

Solve.

Dana solved the inequality $\displaystyle -4x\leq12$ and wrote: $\displaystyle x\leq-3$ .
Substitute $\displaystyle {x}={-5}$ in the inequality $\displaystyle -4x\leq12$ : is it a solution?
What is Dana’s mistake? Write the right solution.

What is the largest whole number that satisfies the inequality $\displaystyle 3x+2<20$ ?

/ – 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

Yael got the marks 78 and 85 in two tests.
She wants the average of the three tests to be at least 85.
At least what mark does she need in the third test?

/ – 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

A taxi ride costs 12 ₪, and 4 ₪ for every kilometre.
Ori has 60 ₪.
At most how many kilometres can he ride in the taxi?

/ – 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

A rectangle’s length is 3 cm more than its width.
The rectangle’s perimeter is at most 50 cm.
What is the largest width the rectangle can have?

/ – 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

Two websites offer films.
On site A you pay 25 ₪ a month, and 5 ₪ for every film.
On site B you pay 10 ₪ for every film, with no monthly fee.
Mark on the graph the point where the two lines meet.
Write an inequality and solve it: from how many films a month is site A cheaper?

\displaystyle y=25+5x

\displaystyle y=10x

Here is the graph of the function $\displaystyle {f(x)}={2x-4}$ .
Mark the point where it meets the $\displaystyle x$ -axis.
Write an inequality and solve it: for which values of $\displaystyle x$ is the graph above the $\displaystyle x$ -axis?

\displaystyle f(x)=2x-4

Here are the graphs of the functions $\displaystyle {f(x)}={3x-1}$ and $\displaystyle {g(x)}={x+5}$ .
Mark the point where they meet.
Write an inequality and solve it: for which values of $\displaystyle x$ is $\displaystyle f(x)>g(x)$ ?

\displaystyle f(x)=3x-1

\displaystyle g(x)=x+5

Formulas: algebra, grade 8

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The linear function

A linear function – $\displaystyle m$ the slope; the line crosses the $\displaystyle y$ -axis at $\displaystyle (0,b)$
$\displaystyle y=mx+b$
The slope of the line through $\displaystyle (x_1,y_1)$ and $\displaystyle (x_2,y_2)$
$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$
Parallel lines have the same slope
$\displaystyle m_1=m_2$
A line through the origin – $\displaystyle {b}={0}$
$\displaystyle y=mx$
A horizontal line – the slope is 0
$\displaystyle y=b$

Word problems

$\displaystyle p$ percent of $\displaystyle x$
$\displaystyle \frac{p}{100}\cdot x$
$\displaystyle s$ the distance, $\displaystyle v$ the speed, $\displaystyle t$ the time
$\displaystyle s$ $\displaystyle =$ $\displaystyle v\cdot t$

Inequalities

Adding or subtracting the same number on both sides – the sign stays
$\displaystyle a+c<b+c$ $\displaystyle a<b$
Multiplying or dividing by a positive number – the sign stays
$\displaystyle a\cdot c<b\cdot c$ $\displaystyle a<b,\ c>0$
Multiplying or dividing by a negative number – the sign turns round
$\displaystyle a\cdot c>b\cdot c$ $\displaystyle a<b,\ c<0$