Examples with solutions for Simplifying and Combining Like Terms: Solving an equation using all techniques

Exercise #1

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

a=? a=?

Video Solution

Step-by-Step Solution

First, let's isolate a from the parentheses in the equation on the right side. We'll remember that minus times minus becomes plus, so we get the equation:

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

Let's continue solving the equation on the right side by adding 2a+3a+a=5a+a=6a 2a+3a+a=5a+a=6a

Now the equation we got is:

a4+7a5=6a+a4 a^4+7a-5=6a+a^4

Let's divide both sides by a4 a^4 and we get:

7a5=6a 7a-5=6a

Now let's move 6a to the left side and the number 5 to the right side, remembering to change the plus and minus signs accordingly.

The equation we got now is:

7a6a=5 7a-6a=5

Let's solve the subtraction and we get:

1a=5 1a=5

Let's divide both sides by 1 and we find that a=5 a=5

Answer

5 5

Exercise #2

4(b2+b)13=6b 4(\frac{b}{2}+b)-\frac{1}{3}=6b

b=? b=\text{?}

Video Solution

Step-by-Step Solution

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

4×b2+4×b13=6b 4\times\frac{b}{2}+4\times b-\frac{1}{3}=6b

Let's solve the multiplication exercise 4×b2=4b2=2b 4\times\frac{b}{2}=\frac{4b}{2}=2b

Now the equation is:

2b+4b13=6b 2b+4b-\frac{1}{3}=6b

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

6b13=6b 6b-\frac{1}{3}=6b

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

13=0 -\frac{1}{3}=0

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

Answer

No solution

Exercise #3

Calculate the value of x:

7x+312=0 -7x+3-\frac{1}{2}=0

Video Solution

Answer

514 \frac{5}{14}

Exercise #4

Find the value of X

4x=1+x -4x=1+x

Video Solution

Answer

15 -\frac{1}{5}

Exercise #5

Solve for x:

5x=12+3x 5x=\frac{1}{2}+3x

Video Solution

Answer

14 \frac{1}{4}

Exercise #6

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

b=? b=\text{?}

Video Solution

Answer

1

Exercise #7

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

y=? y=?

Video Solution

Answer

12 \frac{1}{2}

Exercise #8

Solve for x:

18(x3)+5x=1 \frac{1}{8}(x-3)+5x=1

Video Solution

Answer

20041 \frac{200}{41}

Exercise #9

Solve for x:

x+3(x4)=512x -x+3(x-4)=5-\frac{1}{2}x

Video Solution

Answer

345 \frac{34}{5}

Exercise #10

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

y=? y=?

Video Solution

Answer

1.9 1.9

Exercise #11

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

x=? x=\text{?}

Video Solution

Answer

3-

Exercise #12

Solve for x:

8x+143=08x -8x+\frac{1}{4}-3=0-8x

Video Solution

Answer

There is no solution.

Exercise #13

Solve for x:

x+813x+5=1x -x+8\cdot\frac{1}{3}x+5=1-x

Video Solution

Answer

32 -\frac{3}{2}

Exercise #14

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

x=? x=\text{?}

Video Solution

Answer

60 -60

Exercise #15

(x+2)(2x4)=2x2+x+10 (x+2)(2x-4)=2x^2+x+10

Video Solution

Answer

18 -18

Exercise #16

Solve for x:

8x+3+15=7x+5(1x) -8x+3+\frac{1}{5}=-7x+5(1-x)

Video Solution

Answer

920 \frac{9}{20}

Exercise #17

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 #18

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 #19

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 #20

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}