Chapter 5

Translate the following phrases or sentences into mathematical expressions or equations. Ten times a number is eight more than five times the same number.

Solve and check each equation. $$ 4(y-5)-3 y=-1 \text { for } y. $$

Solve \(\frac{-a b}{2 c}=4 d\) for \(b\)

Write "identity," "contradiction," or "conditional." If you can, find the solution by making an educated guess based on your knowledge of arithmetic. $$ x+4=x-3 $$

For the following problems, solve the linear equations in two variables. $$ y=-2 x+1, \text { if } x=0 $$

Solve the equations. $$ x+8=8 $$

Solve the equations and inequalities for the following problems. $$ 3(2 a+4)=2(a+3) $$

Solve the following linear inequalities. $$ 18 \geq 4(2 x-3)-9 x $$

If nine more than twice a number is forty-six, what is the number?

Translate the following phrases and sentences into mathematical expressions or equations. A number divided by sixteen, plus one, is five.

Solve and check each equation. $$ -2\left(a^{2}+3 a-1\right)+2 a^{2}+7 a=0 \text { for } a. $$

Solve \(\frac{3 x y}{4}=9 x h\) for \(y\)

For the following problems, solve the linear equations in two variables. $$ y=5 x+6, \text { if } x=4 $$

Solve the equations. $$ y-4=4 $$

Solve the equations and inequalities for the following problems. $$ 5(y+3)-(2 y-1)=-5 $$

Solve the following linear inequalities. $$ -\frac{3 b}{16} \leq 4 $$

If nine less than three eighths of a number is two and one fourth, what is the number?

Translate the following phrases and sentences into mathematical expressions or equations. Seven times two more than a number is twenty-one.

Solve and check each equation. $$ -2\left(a^{2}+3 a-1\right)+2 a^{2}+7 a=0 \text { for } a . $$

Solve \(\frac{2 k^{2} m n}{5 p q}=-6 n\) for \(m\)

Write "identity," "contradiction," or "conditional." If you can, find the solution by making an educated guess based on your knowledge of arithmetic. $$ x+x+x=3 x $$

Solve the equations. $$ 2 x=32 $$

Solve the equations and inequalities for the following problems. $$ \frac{-(4 x+3-5 x)}{3}=2 $$

Solve the following linear inequalities. $$ \frac{-7 z+10}{-12}<-1 $$

Twenty percent of a number is \(68 .\) What is the number?

Solve \(8 a+5=3 a-5\) for \(a\).

In the following problems, solve each of the conditional equations. $$ 3 x=42 $$

Write "identity," "contradiction," or "conditional." If you can, find the solution by making an educated guess based on your knowledge of arithmetic. $$ 8 x=0 $$

For the following problems, solve the linear equations in two variables. $$ 3 x+4 y=0, \text { if } x=-3 $$

Solve the equations. $$ 4 x=24 $$

Solve the equations and inequalities for the following problems. $$ \text { Solve } 2 p-6 q+1=-2 \text { for } p $$

Solve the following linear inequalities. $$ -x-\frac{2}{3} \leq \frac{5}{6} $$

Eight more than a quantity is \(37 .\) What is the original quantity?

Solve \(9 y+3(y+6)=15 y+21\) for \(y\).

In the following problems, solve each of the conditional equations. $$ 5 y=75 $$

Write "identity," "contradiction," or "conditional." If you can, find the solution by making an educated guess based on your knowledge of arithmetic. $$ m-7=-5 $$

For the following problems, solve the linear equations in two variables. $$ -2 x+y=1, \text { if } x=\frac{1}{2} $$

Solve the equations and inequalities for the following problems. $$ \text { Solve } p=\frac{n R T}{V} \text { for } T $$

Find the values of \(x\) that satisfy the given continued inequality. $$ 4

If a quantity plus \(85 \%\) more of the quantity is \(62.9,\) what is the original quantity?

Translate the following phrases and sentences into mathematical expressions or equations. Fifty-two is subtracted from some quantity.

Solve \(3 k+2[4(k-1)+3]=63-2 k\) for \(k\).

In the following problems, solve each of the conditional equations. $$ 6 x=48 $$

Solve \(y-3=8\) for \(y\)

For the following problems, solve the linear equations in two variables. $$ 5 x-3 y+1=0, \text { if } x=-6 $$

Solve the equations. $$ 6 m=-30 $$

A company must increase production by \(12 \%\) over last year's production. The new output will be 56 items. What was last year's output?

Classify each equation as an identity or a contradiction. $$ 6 x+3(1-2 x)=3 $$

In the following problems, solve each of the conditional equations. $$ 8 x=56 $$

Solve \(x+9=-4\) for \(x\)