Chapter 2

Solve. For Exercises 1 through \(4,\) write each of the following as equations. The sum of twice a number and 7 is equal to the sum of the number and 6 . Find the number.

Graph each inequality on the number line. $$ x \leq-1 $$

Solve each equation. See Examples 1 and \(2 .\) $$ -4 y+10=-2(3 y+1) $$

Find each number described. For Exercises 1 and 2 , the solutions have been started for you. See Examples 1 and 2 . What number is \(16 \%\) of \(70 ?\) Start the solution: UNDERSTAND the problem. Reread it as many times as needed. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: SOLVE and INTERPRET

Solve each equation. Check each solution. $$ x+7=10 $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(-5 x=-20\)

Substitute the given values into each given formula and solve for the unknown variable. $$ A=b h ; \quad A=45, b=15 $$

Solve. For Exercises 1 through \(4,\) write each of the following as equations. The difference of three times a number and 1 is the same as twice the number. Find the number.

Graph each inequality on the number line. $$ y<0 $$

Find each number described. For Exercises 1 and 2 , the solutions have been started for you. What number is \(88 \%\) of \(1000 ?\) Start the solution: UNDERSTAND the problem. Reread it as many times as needed. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: SOLVE and INTERPRET

Solve each equation. See Examples 1 and \(2 .\) $$ -3 x+1=-2(4 x+2) $$

Solve each equation. Check each solution. $$ x+14=25 $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(-7 x=-49\)

Substitute the given values into each given formula and solve for the unknown variable. $$ d=r t ; \quad d=195, t=3 $$

Solve. For Exercises 1 through \(4,\) write each of the following as equations. Three times a number, minus \(6,\) is equal to two times the number, plus 8 . Find the number.

Graph each inequality on the number line. $$ x>\frac{1}{2} $$

The number 28.6 is what percent of \(52 ?\)

Solve each equation. See Examples 1 and \(2 .\) $$ 15 x-8=10+9 x $$

Solve each equation. Check each solution. $$ x-2=-4 $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(3 x=0\)

Solve. For Exercises 1 through \(4,\) write each of the following as equations. The sum of 4 times a number and -2 is equal to the sum of 5 times the number and \(-2 .\) Find the number.

Graph each inequality on the number line. $$ z \geq-\frac{2}{3} $$

The number 87.2 is what percent of \(436 ?\)

Solve each equation. See Examples 1 and \(2 .\) $$ 15 x-5=7+12 x $$

Solve each equation. Check each solution. $$ y-9=1 $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(2 x=0\)

Substitute the given values into each given formula and solve for the unknown variable. $$ V=l w h ; \quad l=14, w=8, h=3 $$

Twice the difference of a number and 8 is equal to three times the sum of the number and 3 . Find the number.

Graph each inequality on the number line. $$ y<4 $$

The number 45 is \(25 \%\) of what number?

Solve each equation. See Examples 1 and \(2 .\) $$ -2(3 x-4)=2 x $$

Solve each equation. Check each solution. $$ -11=3+x $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(-x=-12\)

Substitute the given values into each given formula and solve for the unknown variable. $$ A=\frac{1}{2} h(B+b) ; \quad A=180, B=11, b=7 $$

Five times the sum of a number and -1 is the same as 6 times the number. Find the number.

Graph each inequality on the number line. $$ x>3 $$

The number 126 is \(35 \%\) of what number?

Solve each equation. Check each solution. $$ -8=8+z $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(-y=8\)

Substitute the given values into each given formula and solve for the unknown variable. $$ A=\frac{1}{2} h(B+b) ; \quad A=60, B=7, b=3 $$

The product of twice a number and three is the same as the difference of five times the number and \(\frac{3}{4}\). Find the number.

Graph each inequality on the number line. $$ -2 \leq m $$

Solve each equation. See Examples 1 and \(2 .\) $$ 5(2 x-1)-2(3 x)=1 $$

Solve each equation. Check each solution. $$ r-8.6=-8.1 $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(\frac{2}{3} x=-8\)

Substitute the given values into each given formula and solve for the unknown variable. $$ \begin{aligned} &P=a+b+c ; \quad P=30, a=8, b=10\\\ &\text { of a triangle) } \end{aligned} $$

If the difference of a number and four is doubled, the result is \(\frac{1}{4}\) less than the number. Find the number.

Graph each inequality on the number line. $$ -5 \geq x $$

Solve each equation. See Examples 1 and \(2 .\) $$ 3(2-5 x)+4(6 x)=12 $$

Solve each equation. Check each solution. $$ t-9.2=-6.8 $$