Examples with solutions for Solving Equations Using All Methods: Opening parentheses

Exercise #1

(7x+3)×(10+4)=238 (7x+3)\times(10+4)=238

Video Solution

Step-by-Step Solution

We begin by solving the addition exercise in the right parenthesis:

(7x+3)+14=238 (7x+3)+14=238

We then multiply each of the terms inside of the parentheses by 14:

(14×7x)+(14×3)=238 (14\times7x)+(14\times3)=238

Following this we solve each of the exercises inside of the parentheses:

98x+42=238 98x+42=238

We move the sections whilst retaining the appropriate sign:

98x=23842 98x=238-42

98x=196 98x=196

Finally we divide the two parts by 98:

9898x=19698 \frac{98}{98}x=\frac{196}{98}

x=2 x=2

Answer

2

Exercise #2

(a+3a)×(5+2)=112 (a+3a)\times(5+2)=112

Calculate a a

Video Solution

Step-by-Step Solution

We begin by solving the two exercises inside of the parentheses:

4a×7=112 4a\times7=112

We then divide each of the sections by 4:

4a×74=1124 \frac{4a\times7}{4}=\frac{112}{4}

In the fraction on the left side we simplify by 4 and in the fraction on the right side we divide by 4:

a×7=28 a\times7=28

Remember that:

a×7=a7 a\times7=a7

Lastly we divide both sections by 7:

a77=287 \frac{a7}{7}=\frac{28}{7}

a=4 a=4

Answer

4

Exercise #3

Solve for X:

3(x2)=4 3(x-2)=4

Video Solution

Answer

103 \frac{10}{3}

Exercise #4

Solve for X:

78(x+4)=3x 7-8(x+4)=-3x

Video Solution

Answer

5 -5

Exercise #5

Solve for X:

34(x2)=6x+4(3x) 3-4(x-2)=6x+4(3-x)

Video Solution

Answer

16 -\frac{1}{6}

Exercise #6

Solve for X:

5(x4)6(7x)=5x 5(x-4)-6(7-x)=5x

Video Solution

Answer

10.33 10.33

Exercise #7

Solve for X:

6+3(x+4)=73(x2) 6+3(x+4)=7-3(x-2)

Video Solution

Answer

56 -\frac{5}{6}

Exercise #8

Solve for X:

6(x+4)4=8(x+5) 6(x+4)-4=8(x+5)

Video Solution

Answer

10 -10

Exercise #9

Solve for X:

7(x4)+3=54(x+5) 7(x-4)+3=5-4(x+5)

Video Solution

Answer

1011 \frac{10}{11}

Exercise #10

Solve for X:

7(x4)=(6x)×3 7(x-4)=(6-x)\times3

Video Solution

Answer

4.6 4.6

Exercise #11

Solve for X:

7(x+5)3(x2)=5 7(x+5)-3(x-2)=5

Video Solution

Answer

9 -9

Exercise #12

Solve for X:


3(x+2)=5(2x) 3(x+2)=5(2-x)

Video Solution

Answer

x=12 x=\frac{1}{2}