8.1 Solve Equations Using the Subtraction and Addition Properties of Equality

Before you get started, take this readiness quiz.

Solve: $n - 12 = 16 .$
If you missed this problem, review the reference.

Translate into algebra ‘five less than $x .’$
If you missed this problem, review the reference.

Is $x = 2$ a solution to $5 x - 3 = 7 ?$
If you missed this problem, review the reference.

Is $y = \frac{2}{3}$ a solution for $9 y + 2 = 6 y ?$

Is $y = \frac{2}{5}$ a solution for $5 y - 3 = 10 y ?$

Solve: $x + 9 = −7 .$

Solve: $x + 16 = −4 .$

Solve: $n - 6 = −7 .$

Solve: $x - 5 = −9 .$

Solve: $p - \frac{1}{3} = \frac{5}{6} .$

Solve: $q - \frac{1}{2} = \frac{1}{6} .$

Solve: $b - 2.8 = 3.6 .$

Solve: $c - 6.9 = 7.1 .$

Solve: $8 y - 4 - 7 y - 7 = 4 .$

Solve: $6 z + 5 - 5 z - 4 = 3 .$

Solve: $5 \left(p - 3\right) - 4 p = −10 .$

Solve: $4 \left(q + 2\right) - 3 q = −8 .$

Solve: $4 \left(2 h - 3\right) - 7 h = −6 - 7 .$

Solve: $2 \left(5 x + 2\right) - 9 x = −2 + 7 .$

Translate and solve: Eleven more than $x$ is equal to $41 .$

Translate and solve: Twelve less than $y$ is equal to $51 .$

Translate and solve: The difference of $4 x$ and $3 x$ is $14 .$

Translate and solve: The difference of $7 a$ and $6 a$ is $−8 .$

Translate into an algebraic equation and solve: The Pappas family has two cats, Zeus and Athena. Together, they weigh $13$ pounds. Zeus weighs $6$ pounds. How much does Athena weigh?

Translate into an algebraic equation and solve: Sam and Henry are roommates. Together, they have $68$ books. Sam has $26$ books. How many books does Henry have?

Translate into an algebraic equation and solve: Eddie paid $\$\text{19},\text{875}$ for his new car. This was $\$\text{1},\text{025}$ less than the sticker price. What was the sticker price of the car?

Translate into an algebraic equation and solve: The admission price for the movies during the day is $\$\text{7}.\text{75} .$ This is $\$\text{3}.\text{25}$ less than the price at night. How much does the movie cost at night?

Determine whether the given value is a solution to the equation.

Is $y = \frac{1}{3}$ a solution of $4 y + 2 = 10 y ?$

Determine whether the given value is a solution to the equation.

Is $u = − \frac{1}{2}$ a solution of $8 u - 1 = 6 u ?$

Solve each equation.

$x + 7 = 12$

Solve each equation.

$b + \frac{1}{4} = \frac{3}{4}$

Solve each equation.

$p + 2.4 = −9.3$

Solve each equation.

$a - 3 = 7$

Solve each equation.

$x - \frac{1}{3} = 2$

Solve each equation.

$y - 3.8 = 10$

Solve each equation.

$x - 15 = −42$

Solve each equation.

$q + \frac{3}{4} = \frac{1}{2}$

Solve each equation.

$y - \frac{3}{4} = \frac{3}{5}$

Solve each equation.

$m + 6 - 8 = 15$

Solve each equation.

$6 x + 8 - 5 x + 16 = 32$

Solve each equation.

$−8 n - 17 + 9 n - 4 = −41$

Solve each equation.

$4 \left(y - 2\right) - 3 y = −6$

Solve each equation.

$5 \left(w + 2.2\right) - 4 w = 9.3$

Solve each equation.

$−8 \left(x - 1\right) + 9 x = −3 + 9$

Solve each equation.

$2 \left(8 m + 3\right) - 15 m - 4 = 3 - 5$

Solve each equation.

$- \left(k + 7\right) + 2 k + 8 = 7$

Solve each equation.

$8 c - 7 \left(c - 3\right) + 4 = −16$

Solve each equation.

$6 \left(9 y - 1\right) - 10 \left(5 y\right) - 3 y = 22$

Translate to an equation and then solve.

The sum of $x$ and $−5$ is $33 .$

Translate to an equation and then solve.

Three less than $y$ is $−19 .$

Translate to an equation and then solve.

Eight more than $p$ is equal to $52 .$

Translate to an equation and then solve.

The difference of $5 c$ and $4 c$ is $60 .$

Translate to an equation and then solve.

The difference of $f$ and $\frac{1}{3}$ is $\frac{1}{12} .$

Translate to an equation and then solve.

The sum of $−9 m$ and $10 m$ is $−25 .$

Translate into an equation and solve.

Jeff read a total of $54$ pages in his English and Psychology textbooks. He read $41$ pages in his English textbook. How many pages did he read in his Psychology textbook?

Translate into an equation and solve.

Eva’s daughter is $5$ years younger than her son. Eva’s son is $12$ years old. How old is her daughter?

Translate into an equation and solve.

For a family birthday dinner, Celeste bought a turkey that weighed $5$ pounds less than the one she bought for Thanksgiving. The birthday dinner turkey weighed $16$ pounds. How much did the Thanksgiving turkey weigh?

Translate into an equation and solve.

Connor’s temperature was $0.7$ degrees higher this morning than it had been last night. His temperature this morning was $101.2$ degrees. What was his temperature last night?

Translate into an equation and solve.

Ron’s paycheck this week was $\$\text{17}.\text{43}$ less than his paycheck last week. His paycheck this week was $\$\text{103}.\text{76} .$ How much was Ron’s paycheck last week?

Construction Miguel wants to drill a hole for a $\frac{5}{\text{8}} -\text{inch}$ screw. The screw should be $\frac{1}{12}$ inch larger than the hole. Let $d$ equal the size of the hole he should drill. Solve the equation $d + \frac{1}{12} = \frac{5}{8}$ to see what size the hole should be.

Write a word sentence that translates the equation $y - 18 = 41$ and then make up an application that uses this equation in its solution.