Question

x/3+x/4=42 solve the equation​

Answer 1

Answer:

Simplifying

(x + -3)(x + -4) = 42

Reorder the terms:

(-3 + x)(x + -4) = 42

Reorder the terms:

(-3 + x)(-4 + x) = 42

Multiply (-3 + x) * (-4 + x)

(-3(-4 + x) + x(-4 + x)) = 42

((-4 * -3 + x * -3) + x(-4 + x)) = 42

((12 + -3x) + x(-4 + x)) = 42

(12 + -3x + (-4 * x + x * x)) = 42

(12 + -3x + (-4x + x2)) = 42

Combine like terms: -3x + -4x = -7x

(12 + -7x + x2) = 42

Solving

12 + -7x + x2 = 42

Solving for variable 'x'.

Reorder the terms:

12 + -42 + -7x + x2 = 42 + -42

Combine like terms: 12 + -42 = -30

-30 + -7x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0

-30 + -7x + x2 = 0

Factor a trinomial.

(-3 + -1x)(10 + -1x) = 0

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying

-3 + -1x = 0

Solving

-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.

-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0

0 + -1x = 0 + 3

-1x = 0 + 3

Combine like terms: 0 + 3 = 3

-1x = 3

Divide each side by '-1'.

x = -3

Simplifying

x = -3

Subproblem 2

Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying

10 + -1x = 0

Solving

10 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.

10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0

0 + -1x = 0 + -10

-1x = 0 + -10

Combine like terms: 0 + -10 = -10

-1x = -10

Divide each side by '-1'.

x = 10

Simplifying

x = 10

Solution

x = {-3, 10}

Answer 2

Answer:

$\frac{x}{3} + \frac{x}{4} = 42 \\ \\ x( \frac{7}{12} ) = 42 \\ \\ x = 12 \times 6 = 72$