Question

4(2x+6)=5(x+5)+2 Infinite solutions Infinite solutions No solution No solution One solution; x=0One solution; x is equal to 0 One solution; x=1

Answer 1

Answer:

x = 1

Step-by-step explanation:

Solve for x:

4 (2 x + 6) = 5 (x + 5) + 2

Hint: | Distribute 5 over x + 5.

5 (x + 5) = 5 x + 25:

4 (2 x + 6) = 5 x + 25 + 2

Hint: | Group like terms in 5 x + 2 + 25.

Grouping like terms, 5 x + 2 + 25 = 5 x + (25 + 2):

4 (2 x + 6) = 5 x + (25 + 2)

Hint: | Evaluate 25 + 2.

25 + 2 = 27:

4 (2 x + 6) = 5 x + 27

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

8 x + 24 = 5 x + 27

Hint: | Move terms with x to the left hand side.

Subtract 5 x from both sides:

(8 x - 5 x) + 24 = (5 x - 5 x) + 27

Hint: | Combine like terms in 8 x - 5 x.

8 x - 5 x = 3 x:

3 x + 24 = (5 x - 5 x) + 27

Hint: | Look for the difference of two identical terms.

5 x - 5 x = 0:

3 x + 24 = 27

Hint: | Isolate terms with x to the left hand side.

Subtract 24 from both sides:

3 x + (24 - 24) = 27 - 24

Hint: | Look for the difference of two identical terms.

24 - 24 = 0:

3 x = 27 - 24

Hint: | Evaluate 27 - 24.

27 - 24 = 3:

3 x = 3

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 3 x = 3 by 3:

(3 x)/3 = 3/3

Hint: | Any nonzero number divided by itself is one.

3/3 = 1:

x = 3/3

Hint: | Any nonzero number divided by itself is one.

3/3 = 1:

Answer:  x = 1