2.1 Solve equations using the subtraction and addition properties  (Page 5/6)

Is $y=\frac{5}{3}$ a solution of
$6y+10=12y$ ?

Is $x=\frac{9}{4}$ a solution of
$4x+9=8x$ ?

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

Is $v=-\frac{1}{3}$ a solution of
$9v-2=3v$ ?

$x+24=35$

$x+17=22$

$y+45=\mathrm{-66}$

$y+39=\mathrm{-83}$

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

$a+\frac{2}{5}=\frac{4}{5}$

$p+2.4=\mathrm{-9.3}$

$m+7.9=11.6$

$a-45=76$

$a-30=57$

$m-18=\mathrm{-200}$

$m-12=\mathrm{-12}$

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

$x-\frac{1}{5}=4$

$y-3.8=10$

$y-7.2=5$

$x-165=\mathrm{-420}$

$z-101=\mathrm{-314}$

$z+0.52=\mathrm{-8.5}$

$x+0.93=\mathrm{-4.1}$

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

$p+\frac{1}{3}=\frac{5}{6}$

$p-\frac{2}{5}=\frac{2}{3}$

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

$c+31-10=46$

$m+16-28=5$

$9x+5-8x+14=20$

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

$\mathrm{-6}x-11+7x-5=\mathrm{-16}$

$\mathrm{-8}n-17+9n-4=\mathrm{-41}$

$5\left(y-6\right)-4y=\mathrm{-6}$

$9\left(y-2\right)-8y=\mathrm{-16}$

$8\left(u+1.5\right)-7u=4.9$

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

$6a-5\left(a-2\right)+9=\mathrm{-11}$

$8c-7\left(c-3\right)+4=\mathrm{-16}$

$6\left(y-2\right)-5y=4\left(y+3\right)$
$-4\left(y-1\right)$

$9\left(x-1\right)-8x=\mathrm{-3}\left(x+5\right)$
$+3\left(x-5\right)$

$3(5n-1)-14n+9$
$=10\left(n-4\right)-6n-4\left(n+1\right)$

$2(8m+3)-15m-4$
$=9\left(m+6\right)-2\left(m-1\right)-7m$

$\text{−}\left(j+2\right)+2j-1=5$

$\text{−}\left(k+7\right)+2k+8=7$

$\text{−}\left(\frac{1}{4}a-\frac{3}{4}\right)+\frac{5}{4}a=\mathrm{-2}$

$\text{−}\left(\frac{2}{3}d-\frac{1}{3}\right)+\frac{5}{3}d=\mathrm{-4}$

$8(4x+5)-5(6x)-x$
$=53-6(x+1)+3(2x+2)$

$6(9y-1)-10(5y)-3y$
$=22-4\left(2y-12\right)+8\left(y-6\right)$

Nine more than $x$ is equal to 52.

The sum of x and $\mathrm{-15}$ is 23.

Ten less than m is $\mathrm{-14}$ .

Three less than y is $\mathrm{-19}$ .

The sum of y and $\mathrm{-30}$ is 40.

Twelve more than p is equal to 67.

The difference of $9x\text{and}8x$ is 107.

The difference of $5c\text{and}4c$ is 602.

The difference of $n$ and $\frac{1}{6}$ is $\frac{1}{2}$ .

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

The sum of $\mathrm{-4}n$ and $5n$ is $\mathrm{-82}$ .

The sum of $\mathrm{-9}m$ and $10m$ is $\mathrm{-95}$ .

Distance Avril rode her bike a total of 18 miles, from home to the library and then to the beach. The distance from Avril’s house to the library is 7 miles. What is the distance from the library to the beach?

Reading Jeff read a total of 54 pages in his History and Sociology textbooks. He read 41 pages in his History textbook. How many pages did he read in his Sociology textbook?

Age Eva’s daughter is 15 years younger than her son. Eva’s son is 22 years old. How old is her daughter?

Age Pablo’s father is 3 years older than his mother. Pablo’s mother is 42 years old. How old is his father?

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

Weight Allie weighs 8 pounds less than her twin sister Lorrie. Allie weighs 124 pounds. How much does Lorrie weigh?

Health 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?

Health The nurse reported that Tricia’s daughter had gained 4.2 pounds since her last checkup and now weighs 31.6 pounds. How much did Tricia’s daughter weigh at her last checkup?

Salary Ron’s paycheck this week was $17.43 less than his paycheck last week. His paycheck this week was $103.76. How much was Ron’s paycheck last week?

Textbooks Melissa’s math book cost $22.85 less than her art book cost. Her math book cost $93.75. How much did her art book cost?

Construction Miguel wants to drill a hole for a $\frac{5}{8}$ inch screw. The hole should be $\frac{1}{12}$ inch smaller than the screw. 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.

Baking Kelsey needs $\frac{2}{3}$ cup of sugar for the cookie recipe she wants to make. She only has $\frac{3}{8}$ cup of sugar and will borrow the rest from her neighbor. Let $s$ equal the amount of sugar she will borrow. Solve the equation $\frac{3}{8}+s=\frac{2}{3}$ to find the amount of sugar she should ask to borrow.

Is $\mathrm{-8}$ a solution to the equation $3x=16-5x$ ? How do you know?

What is the first step in your solution to the equation $10x+2=4x+26$ ?