Chapter 11

When four is decreased by three times some number, the result is equal to one less than twice the number. What is the number?

Solve each equation. $$ y-6=2 $$

Solve each equation. Be sure to check each result. $$ 8 x=81 $$

Verify that each given value is a solution to the given equation. $$2 m-1=1, m=1$$

Simplify each expression by combining like terms. $$7 h+3 a-10 k+6 a-2 h-5 k-3 k$$

In an algebraic expression, terms are separated by ______ signs and factors are separated by ______ signs.

Translate each phrase or sentence to a mathematical expression or equation. A number plus seven.

In the expression \(-5 n\), how many \(n\) 's are indicated?

When twice a number is subtracted from one, the result is equal to twenty-one more than the number. What is the number?

Solve each equation. $$ m+8=-1 $$

Solve each equation. Be sure to check each result. $$ 10 x=120 $$

Verify that each given value is a solution to the given equation. $$5 y+6=-14, y=-4$$

Simplify each expression by combining like terms. $$4 x-8 y-3 z+x-y-z-3 y-2 z$$

Translate each phrase or sentence to a mathematical expression or equation. A number increased by one.

In the expression \(-10 y\), how many \(y\) 's are indicated?

The perimeter of a rectangle is 36 inches. If the length of the rectangle is 6 inches more than the width, find the length and width of the rectangle.

Solve each equation. $$ -5+a=-4 $$

Solve each equation. Be sure to check each result. $$ 11 x=121 $$

Verify that each given value is a solution to the given equation. $$3 x+2-7 x=-5 x-6, x=-8$$

Simplify each expression by combining like terms. $$11 w+3 x-6 w-5 w+8 x-11 x$$

Translate each phrase or sentence to a mathematical expression or equation. A number decreased by ten.

For problems \(17-46\), find the value of each expression. $$ 5 a-2 s, \text { if } a=-5 \text { and } s=1 $$

The perimeter of a rectangle is 48 feet. Find the length and the width of the rectangle if the length is 8 feet more than the width.

Solve each equation. $$ 4 x=104 $$

Solve each equation. Be sure to check each result. $$ -6 a=48 $$

Verify that each given value is a solution to the given equation. $$-6 a+3+3 a=4 a+7-3 a, a=-1$$

Simplify each expression by combining like terms. $$15 r-6 s+2 r+8 s-6 r-7 s-s-2 r$$

Translate each phrase or sentence to a mathematical expression or equation. Negative seven added to some number.

For problems \(17-46\), find the value of each expression. $$ 7 n-3 r, \text { if } n=-6 \text { and } r=2 $$

The sum of three consecutive integers is \(48 .\) What are they?

Solve each equation. $$ 6 y+3=-21 $$

Solve each equation. Be sure to check each result. $$ -9 y=54 $$

Verify that each given value is a solution to the given equation. $$-8+x=-8, x=0$$

Simplify each expression by combining like terms. $$|-7| m+|6| m+|-3| m$$

Specify each term. $$8 s+2 r-7 t$$

Translate each phrase or sentence to a mathematical expression or equation. Negative nine added to a number.

For problems \(17-46\), find the value of each expression. $$ 9 x+2 y-3 s, \text { if } x=-2, y=5, \text { and } s=-3 $$

The sum of three consecutive integers is \(-27 .\) What are they?

Solve each equation. $$ \frac{5 m}{6}=\frac{10}{2} $$

Solve each equation. Be sure to check each result. $$ -3 y=-42 $$

Verify that each given value is a solution to the given equation. $$8 b+6=6-5 b, b=0$$

Simplify each expression by combining like terms. $$|-2| x+|-8| x+|10| x$$

Specify each term. $$m-3 n-4 a+7 b$$

Translate each phrase or sentence to a mathematical expression or equation. A number plus the opposite of six.

For problems \(17-46\), find the value of each expression. $$ 10 a-2 b+5 c \text { , if } a=0, b=-6 \text { , and } c=8 $$

The sum of five consecutive integers is zero. What are they?

Solve each equation. $$ \frac{7 y}{8}+\frac{1}{4}=\frac{-13}{4} $$

Solve each equation. Be sure to check each result. $$ -5 a=-105 $$

Verify that each given value is a solution to the given equation. $$4 x-5=6 x-20, x=\frac{15}{2}$$

Simplify each expression by combining like terms. $$(-4+1) k+(6-3) k+(12-4) h+(5+2) k$$