Free Printable Solving Multi-Step Inequalities

1.

$3n-7\le56$

a)

$n\le16.333...$

b)

$n\le21$

c)

$n\ge63$

d)

$n\ge-14$

2.

$-3n-7\le56$

a)

$n\le-16.333...$

b)

$n\le21$

c)

$n\ge-21$

d)

$n\le-14$

3.

TRUE or FALSE:

When solving an inequality, you leave the inequality symbol the same even if you divide by a negative coefficient to isolate the variable.

a)

TRUE

b)

FALSE

c)

There is not enough information to determine this.

4.

Annalise solved an inequality in class and got an answer of $x\ge-13.$ Which subset of numbers below shows some of the many possible solutions to the problem she solved?

a)

$\left\{-\frac{44}{3},\ -\frac{21}{2},\ -7.25,\ 7.25\right\}$

b)

$\left\{-\frac{51}{4},\ -\frac{17}{2},\ 0,\ 8.15\right\}$

c)

$\left\{-\frac{71}{5},\ -\frac{23}{2},\ 0,\ \frac{3}{2}\right\}$

5.

$-10m+2<-18$

a)

$m<2$

b)

$m<1.6$

c)

$m>2$

d)

$m>1.6$

6.

$4\left(2x-1\right)>-7+2x$

a)

$x<-2$

b)

$x<-\frac{1}{2}$

c)

$x>-2$

d)

$x>-\frac{1}{2}$

7.

$4\left(y+4\right)\le16$

a)

$y\le0$

b)

No Solution

c)

$y\le2$

8.

$2\left(2x+13\right)\ge4\left(-6+x\right)$

a)

$x\ge-6.25$

b)

All Real Numbers

c)

No Solution

d)

$x\le0$

9.

$2h+11>-7+4h-16$

a)

$h<17$

b)

$h<6$

c)

$h>-17$

d)

$h>-6$

10.

What is the FIRST step to solving this inequality?

$-4\left(x-9\right)+2x\ge-27$

a)

Subtract 2x on both sides

b)

Distribute: multiply -4 by x and by -9

c)

Add x to 2x

d)

Add 9 to both sides

11.

In which inequality below will you have to flip the inequality symbol in your answer to get the correct solution set?

a)

$-3\ +x\ \le18$

b)

$x-11>-20$

c)

$2x\ge-30$

d)

$\frac{x}{-5}>10$

12.

The first step in solving this inequality is to use the distributive property.

$4\left(n-8\right)>-26$

a)

True

b)

False

13.

The first step in solving this inequality is to combine like terms.

$9\left(n+1\right)\le-26+n$

a)

True

b)

False

Solving Multi-Step Inequalities

Total questions: 13

Worksheet time: 54mins

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