Examples with solutions for Solving an Equation by Multiplication/ Division: Solving an equation using all techniques

Exercise #1

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

a=? a=\text{?}

Video Solution

Step-by-Step Solution

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

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

12a24=27a -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 -24=27a+12a

Let's group the terms on the right side:

24=39a -24=39a

Let's divide both sides by 39:

2439=39a39 -\frac{24}{39}=\frac{39a}{39}

2439=a -\frac{24}{39}=a

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

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

Answer

813 -\frac{8}{13}

Exercise #2

14a+5=20+a \frac{1}{4}a+5=20+a

a=? a=\text{?}

Video Solution

Answer

20 -20

Exercise #3

4y7+6y=310y 4y-7+6y=3-10y

y=? y=?

Video Solution

Answer

12 \frac{1}{2}

Exercise #4

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

b=? b=\text{?}

Video Solution

Answer

1

Exercise #5

6c+7+4c=3(c1) 6c+7+4c=3(c-1)

c=? c=\text{?}

Video Solution

Answer

137 -1\frac{3}{7}

Exercise #6

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

y=? y=\text{?}

Video Solution

Answer

115 \frac{1}{15}

Exercise #7

a4+7a5=2a+a4+3a(a) a^4+7a-5=2a+a^4+3a-(-a)

a=? a=?

Video Solution

Answer

5 5

Exercise #8

12y+3y10+7(y4)=2y 12y+3y-10+7(y-4)=2y

y=? y=?

Video Solution

Answer

1.9 1.9

Exercise #9

13(x+9)=4+23x \frac{1}{3}(x+9)=4+\frac{2}{3}x

x=? x=\text{?}

Video Solution

Answer

3-

Exercise #10

2x+4513x=5(x+7) 2x+45-\frac{1}{3}x=5(x+7)

x=? x=\text{?}

Video Solution

Answer

3

Exercise #11

74(x)+2x5(x+3)=x -\frac{7}{4}(-x)+2x-5(x+3)=-x

x=? x=\text{?}

Video Solution

Answer

60 -60

Exercise #12

(x+4)(3x14)=3(x2+5) (x+4)(3x-\frac{1}{4})=3(x^2+5)

x=? x=?

Video Solution

Answer

11747 1\frac{17}{47}

Exercise #13

4(x2+5)=(x+7)(4x9)+5 -4(x^2+5)=(-x+7)(4x-9)+5

x=? x=?

Video Solution

Answer

1137 1\frac{1}{37}

Exercise #14

x4y+4xy+3x4y15=20xyx2y -\frac{x}{4y}+\frac{4x}{y}+\frac{3x}{4y}-15=20\frac{x}{y}-\frac{x}{2y}

xy=? \frac{x}{y}=?

Video Solution

Answer

1 -1

Exercise #15

150+75m+m8m3=(9005m2)112 150+75m+\frac{m}{8}-\frac{m}{3}=(900-\frac{5m}{2})\cdot\frac{1}{12}

m=? m=\text{?}

Video Solution

Answer

1 -1

Exercise #16

t+2(4+t)(t+5)=(t5)(2t3) -t+2(4+t)(t+5)=(t-5)(2t-3)

t=? t=\text{?}

Video Solution

Answer

56 -\frac{5}{6}