Solve for x

2x/3 + 2 = 16

21

Step-by-step explanation:

The first term is, 4x2 its coefficient is 4.

The middle term is, - 12x its coefficient is - 12.

The last term, "the constant", is - 7

Step-1 : Multiply the coefficient of the first term by the constant 4 • - 7 = - 28

Step-2 : Find two factors of - 28 whose sum equals the coefficient of the middle term, which is - 12.

-28 + 1 = - 27

-14 + 2 = - 12 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 14 and 2

4x2 - 14x + 2x - 7

Step-4 : Add up the first 2 terms, pulling out like factors:

2x • (2x-7)

Add up the last 2 terms, pulling out common factors:

1 • (2x-7)

Step-5 : Add up the four terms of step 4:

(2x+1) • (2x-7)

Which is the desired factorization

Equation at the end of step 1:

(2x - 7) • (2x + 1) = 0

Step 2:

Theory - Roots of a product:

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : 2x-7 = 0

Add 7 to both sides of the equation:

2x = 7

Divide both sides of the equation by 2:

x = 21

2x/3 + 2 = 16

=21

Step-by-step explanation:

Standard form:

2

3

x - 14 = 0

Factorization:

2

3 (x - 21) = 0

Solutions:

x = 42

2

= 21