Problems -Set 1

1. Solve for $y$.

   $-2y+26=-7(y-3)$

   Simplify your answer as much as possible.

2. Solve for $u$.

   $-2(9u-7)+6u=2(u+9)$

   Simplify your answer as much as possible.

3. Solve for $v$.

   $-\dfrac{1}{3}-\dfrac{1}{2}v=\dfrac{4}{9}$

   Simplify your answer as much as possible.

4. Solve the inequality for $x$.

   $20\le -6x-10$

   Simplify your answer as much as possible.

5. Solve the compound inequality.

   $-4y\ge 12$  and  $2y-4 \le -16$

   Write the solution in interval notation.

6. Solve for $y$.

   $3|y+7|-10=-49$

   If there is more than one solution, separate them with commas.

7. Solve for $v$.

   $|5v+7|=|5v+13|$

   If there is more than one solution, separate them with commas.

Answer key

1. $y=-1$

2. $u=-\dfrac{2}{7}$

3. $v=-\dfrac{14}{9}$

4. $x\le -5$. Answer can also be written as $-5\ge x$.

5. $(-\infty, -6]$

6. No solution

7. $v=-2$

Problems -Set 2

1. Solve for $u$.

   $8(u-5)=5u-37$

   Simplify your answer as much as possible.

2. Solve for $x$.

   $4(x-1)=7x+7-2(-3x-2)$

   Simplify your answer as much as possible.

3. Solve for $x$.

   $\dfrac{9}{5}=-\dfrac{7}{3}x-\dfrac{9}{2}$

   Simplify your answer as much as possible.

4. Solve the inequality for $y$.

   $2y+10\gt-2$

   Simplify your answer as much as possible.

5. Solve the compound inequality.

   $3w+4\le -14$  or  $2w-2 \gt 4$

   Write the solution in interval notation.

6. Solve for $v$.

   $5|v-4|+10=90$

   If there is more than one solution, separate them with commas.

7. Solve for $x$.

   $|6-3x|=|2x-5|$

   If there is more than one solution, separate them with commas.

Answer key:

1. $u=1$

2. $x=-\dfrac{5}{3}$

3. $-\dfrac{27}{10}$

4. $y\gt -6$

5. $(-\infty, -6]\cup (3, \infty)$

6. $v=20, -12$

7. $x=\dfrac{11}{5}, 1$