Chapter 5

For the following problems, solve the linear equations in two variables. $$ -4 x-4 y=4, \text { if } y=7 $$

Solve the equations. $$ -5 x=-30 $$

Solve the equations and inequalities for the following problems. $$ a-8 \geq 4 $$

Find the values of \(x\) that satisfy the given continued inequality. $$ 0 \leq 1-6 x \leq 7 $$

A company has determined that it must increase production of a certain line of goods by \(1 \frac{1}{2}\) times last year's production. The new output will be 2885 items. What was last year's output?

For the following problems, translate the following phrases or sentences into mathematical expressions or equations. A quantity less four.

Classify each equation as an identity or a contradiction. $$ -8 m+4(2 m-7)=28 $$

In the following problems, solve each of the conditional equations. $$ 4 x=56 $$

Solve \(m+6=0\) for \(m\).

For the following problems, solve the linear equations in two variables. $$ 2 x+6 y=1, \text { if } y=0 $$

Solve the equations. $$ -8 y=-72 $$

Solve the equations and inequalities for the following problems. $$ -3 a+1<-5 $$

Find the values of \(x\) that satisfy the given continued inequality. $$ -5 \leq \frac{2 x+1}{3} \leq 10 $$

A proton is about 1837 times as heavy as an electron. If an electron weighs 2.68 units, how many units does a proton weigh?

For the following problems, translate the following phrases or sentences into mathematical expressions or equations. Eight more than a number.

Classify each equation as an identity or a contradiction. $$ 3(2 x-4)-2(3 x+1)+14=0 $$

In the following problems, solve each of the conditional equations. $$ 3 x=93 $$

Solve \(g-7.2=1.3\) for \(g\)

For the following problems, solve the linear equations in two variables. $$ -x-y=0, \text { if } y=\frac{14}{3} $$

Solve the equations. $$ -x=6 $$

Solve the equations and inequalities for the following problems. $$ -2(a+6) \leq-a+11 $$

Find the values of \(x\) that satisfy the given continued inequality. $$ 9<\frac{-4 x+5}{-2}<14 $$

Neptune is about 30 times as far from the sun as is the Earth. If it takes light 8 minutes to travel from the sun to the Earth. how manv minutes does it take to travel to Neptune? ? mom the sun to tharth. how manv minutes does it take to Neptunn?

For the following problems, translate the following phrases or sentences into mathematical expressions or equations. A number plus seven.

Classify each equation as an identity or a contradiction. $$ -5(x+6)+8=3[4-(x+2)]-2 x $$

In the following problems, solve each of the conditional equations. $$ 5 a=-80 $$

Solve \(f+2 d=5 d\) for \(f\)

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

Solve the equations. $$ -y=-10 $$

Solve the equations and inequalities for the following problems. $$ \frac{-4 x-3}{3}>-9 $$

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

The radius of the sun is about \(695,202 \mathrm{~km}\) (kilometers). That is about 109 times as big as the radius of the Earth. What is the radius of the earth?

For the following problems, translate the following phrases or sentences into mathematical expressions or equations. A number minus three.

For the following problems, solve each conditional equation. If the equation is not conditional, identify it as an identity or a contradiction. $$ 3 x+1=16 $$

In the following problems, solve each of the conditional equations. $$ 9 m=-108 $$

Solve \(x+8 y=2 y-1\) for \(x\).

Solve the equations. $$ 3 x+7=19 $$

Translate the phrases or sentences into mathematical expressions or equations for the following problems. Three added to twice a number.

For the following problems, solve the inequalities. $$ x+7<12 $$

The perimeter of a triangle is \(105 \mathrm{~cm}\). If each of the two legs is exactly twice the length of the base, how long is each leg?

For the following problems, translate the following phrases or sentences into mathematical expressions or equations. Negative five plus an unknown quantity,

For the following problems, solve each conditional equation. If the equation is not conditional, identify it as an identity or a contradiction. $$ 6 y-4=20 $$

In the following problems, solve each of the conditional equations. $$ 6 p=-108 $$

Solve \(y+4 x-1=5 x+8\) for \(y\)

For the following problems, solve the linear equations in two variables. $$ y+\frac{3}{4}=x, \text { if } x=\frac{9}{4} $$

Solve the equations. $$ 6 x-1=29 $$

Translate the phrases or sentences into mathematical expressions or equations for the following problems. Eight less than two thirds of a number.

For the following problems, solve the inequalities. $$ y-5 \leq 8 $$

A lumber company has contracted to cut boards into two pieces so that one piece is three times the length of the other piece. If a board is 12 feet long, what is the length of each piece after cutting?

For the following problems, translate the following phrases or sentences into mathematical expressions or equations. Negative sixteen minus some quantity.