Solving Equations by using Addition/ Subtraction: Solving an equation using all techniques

Question 1

$$ -3(4a+8)=27a $$

$a=\text{?}$

Question 2

$4(\frac{b}{2}+b)-\frac{1}{3}=6b$

$b=\text{?}$

Question 3

Solve for X:

$$ 8+2(x+1)=7x $$

Question 4

Solve for X:

$$ 3-(x-4)+8x=14 $$

Question 5

$\frac{1}{4}a+5=20+a$

$a=\text{?}$

Examples with solutions for Solving Equations by using Addition/ Subtraction: Solving an equation using all techniques

Exercise #1

$-3(4a+8)=27a$

$a=\text{?}$

Video Solution

Step-by-Step Solution

To open the parentheses on the left side, we'll use the formula:

$-a\left(b+c\right)=-ab-ac$

$-12a-24=27a$

We'll arrange the equation so that the terms with 'a' are on the right side, and maintain the plus and minus signs during the transfer:

$-24=27a+12a$

Let's group the terms on the right side:

$-24=39a$

Let's divide both sides by 39:

$-\frac{24}{39}=\frac{39a}{39}$

$-\frac{24}{39}=a$

Note that we can reduce the fraction since both numerator and denominator are divisible by 3:

$-\frac{8}{13}=a$

Answer

$-\frac{8}{13}$

Exercise #2

$4(\frac{b}{2}+b)-\frac{1}{3}=6b$

$b=\text{?}$

Video Solution

Step-by-Step Solution

First, we'll open the parentheses by multiplying each term by 4:

$4\times\frac{b}{2}+4\times b-\frac{1}{3}=6b$

Let's solve the multiplication exercise $4\times\frac{b}{2}=\frac{4b}{2}=2b$

Now the equation is:

$2b+4b-\frac{1}{3}=6b$

We'll combine the left side between the two b terms and get:

$6b-\frac{1}{3}=6b$

We'll reduce both sides by 6b and get:

$-\frac{1}{3}=0$

Since the result obtained is impossible, the exercise has no solution.

Answer

No solution

Exercise #3

Solve for X:

$8+2(x+1)=7x$

Video Solution

Answer

$2$

Exercise #4

Solve for X:

$3-(x-4)+8x=14$

Video Solution

Answer

$1$

Exercise #5

$\frac{1}{4}a+5=20+a$

$a=\text{?}$

Video Solution

Answer

$-20$

Question 1

$$ 4y-7+6y=3-10y $$

$$ y=? $$

Question 2

$$ 37b+6b+56=90+9 $$

$b=\text{?}$

Question 3

$$ 6c+7+4c=3(c-1) $$

$c=\text{?}$

Question 4

$$ 7y+10y+5=2(y+3) $$

$y=\text{?}$

Question 5

Solve for X:

$6\cdot(5+2x)=3x-6$

Exercise #6

$4y-7+6y=3-10y$

$y=?$

Video Solution

Answer

$\frac{1}{2}$

Exercise #7

$37b+6b+56=90+9$

$b=\text{?}$

Video Solution

Answer

Exercise #8

$6c+7+4c=3(c-1)$

$c=\text{?}$

Video Solution

Answer

$-1\frac{3}{7}$

Exercise #9

$7y+10y+5=2(y+3)$

$y=\text{?}$

Video Solution

Answer

$\frac{1}{15}$

Exercise #10

Solve for X:

$6\cdot(5+2x)=3x-6$

Video Solution

Answer

$-4$

Question 1

Solve for X:

$(3-2x)\cdot5=4+12x$

Question 2

$$ a^4+7a-5=2a+a^4+3a-(-a) $$

$$ a=? $$

Question 3

$3x+\frac{2}{3}=4(x+\frac{1}{12})$

$x=\text{?}$

Question 4

$$ 12y+3y-10+7(y-4)=2y $$

$$ y=? $$

Question 5

$\frac{1}{3}(x+9)=4+\frac{2}{3}x$

$x=\text{?}$

Exercise #11

Question 2

Solve for X:

$\frac{1}{2}\cdot(8-x)+\frac{1}{2}x=12-x$

Question 3

Solve for X:

$\frac{1}{4}(x-16)+\frac{3}{4}x=8x-11$

Question 4

$$ $$ (x+2)(2x-4)=2x^2+x+10 $$

Question 5

$2x+45-\frac{1}{3}x=5(x+7)$

$x=\text{?}$

Exercise #16

Exercise #20

$2x+45-\frac{1}{3}x=5(x+7)$

$x=\text{?}$