Question

For what value or values of x are the expressions below equivalent? Explain your reasoning. 4x+5+x+9 and 9x+10

Answer 1

For the expressions 4x+5+x+9 and 9x+10 to be equivalent, they must have the same value for any value of x.

So we can set the two expressions equal to each other and solve for x.

4x + 5 + x + 9 = 9x + 10

Simplifying the left side:

5x + 14 = 9x + 10

Subtracting 5x from both sides:

14 = 4x + 10

Subtracting 10 from both sides:

4 = 4x

Dividing both sides by 4:

x = 1

So the expressions 4x+5+x+9 and 9x+10 are equivalent when x = 1.