Chapter 11

Specify each term. $$7 a-2 b-3 c-4 d$$

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

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

The sum of five consecutive integers is \(-5 .\) What are they?

Solve each equation. $$ 6 x+5=4 x-11 $$

Solve each equation. Be sure to check each result. $$ 2 m=-62 $$

Verify that each given value is a solution to the given equation. $$-3 y+7=2 y-15, y=\frac{22}{5}$$

Simplify each expression by combining like terms. $$(-5+3) a-(2+5) b-(3+8) b$$

Specify each term. $$-6 a-5 b$$

Translate each phrase or sentence to a mathematical expression or equation. A number minus the opposite of negative one.

For problems \(17-46\), find the value of each expression. $$ -3 m-4 n+5, \text { if } m=-1 \text { and } n=-1 $$

The perimeter of a rectangle is 18 meters. Find the length and width of the rectangle if the length is 1 meter more than three times the width.

Solve each equation. $$ 4 y-8-6 y=3 y+1 $$

Solve each equation. Be sure to check each result. $$ 3 m=-54 $$

Simplify each expression by combining like terms. $$5 \star+2 \Delta+3 \Delta-8 \star$$

Translate each phrase or sentence to a mathematical expression or equation. A number minus the opposite of negative twelve.

For problems \(17-46\), find the value of each expression. $$ m-4, \text { if } m=4 $$

Three consecutive even integers add to -36 . What are they?

Solve each equation. Be sure to check each result. $$ \frac{x}{4}=7 $$

Translate each phrase or sentence to a mathematical expression or equation. Eleven added to three times a number.

Find the length and width of a rectangle with perimeter 74 inches, if the width of the rectangle is 8 inches less than twice the length.

The perimeter of a rectangle is 38 feet. Find the length and width of the rectangle if the length is 5 feet less than three times the width.

Solve each equation. Be sure to check each result. $$ \frac{y}{3}=11 $$

Simplify each expression by combining like terms. $$16 x-12 y+5 x+7-5 x-16-3 y$$

Write \(1 m\) in a simpler way.

Translate each phrase or sentence to a mathematical expression or equation. Six plus five times an unknown number.

For problems \(17-46\), find the value of each expression. $$ -x+2 y, \text { if } x=-7 \text { and } y=-1 $$

Find the length and width of a rectangle with perimeter 18 feet, if the width of the rectangle is 7 feet less than three times the length.

Four numbers add to \(-2 .\) The second number is three more than twice the negative of the first number. The third number is six less than the first number. The fourth number is eleven less than twice the first number. Find the numbers.

Solve each equation. Be sure to check each result. $$ \frac{-z}{6}=-14 $$

Simplify each expression by combining like terms. $$-3 y+4 z-11-3 z-2 y+5-4(8-3)$$

Translate each phrase or sentence to a mathematical expression or equation. Twice a number minus seven equals four.

For problems \(17-46\), find the value of each expression. $$ -a+3 b-6, \text { if } a=-3 \text { and } b=0 $$

A person makes a mistake when copying information regarding a particular rectangle. The copied information is as follows: The length of a rectangle is 5 inches less than two times the width. The perimeter of the rectangle is 2 inches. What is the mistake?

Solve each equation. Be sure to check each result. $$ \frac{-w}{5}=1 $$

Convert \(\frac{24}{11}\) to a mixed number.

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

Translate each phrase or sentence to a mathematical expression or equation. Ten times a quantity increased by two is nine.

For problems \(17-46\), find the value of each expression. $$ 5 x-4 y-7 y+y-7 x, \text { if } x=1 \text { and } y=-2 $$

A person makes a mistake when copying information regarding a particular triangle. The copied information is as follows: Two sides of a triangle are the same length. The third side is 10 feet less than three times the length of one of the other sides. The perimeter of the triangle is 5 feet. What is the mistake?

Solve each equation. Be sure to check each result. $$ 3 m-1=-13 $$

Determine the missing numerator: \(\frac{3}{8}=\frac{?}{64}\).

In the expression \(-7 c\), how many \(c\) 's are indicated?

Translate each phrase or sentence to a mathematical expression or equation. When fourteen is added to two times a number the result is six.

For problems \(17-46\), find the value of each expression. $$ 2 a-6 b-3 a-a+2 b, \text { if } a=4 \text { and } b=-2 $$

The perimeter of a triangle is 75 meters. If each of two legs is exactly twice the length of the shortest leg, how long is the shortest leg?

Solve each equation. Be sure to check each result. $$ 4 x+7=-17 $$

Simplify \(\frac{\frac{5}{6}-\frac{1}{4}}{\frac{1}{12}}\).

Find the value of each expression. $$2 m-6 n, \text { if } m=-3 \text { and } n=4$$

Translate each phrase or sentence to a mathematical expression or equation. Four times a number minus twenty-nine is eleven.