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## Question Explanations For

##
*Heart of Algebra (Algebraic Expressions)*

1 2 3 4 5 6 7 8 910

## 1.

The Correct Answer is (A) —
Simply add the coefficients of the shared variable, $x$: $x+3x=4x$. Remember that when adding coefficients, the variable remains the same! The correct answer choice is A.

## 2.

The Correct Answer is (D) —
As with the previous problem, add the coefficients of the shared variable, and add the constants separately: 17-6h-23+2h = -6h+2h+17-23= -4h-6. The correct answer choice is D.

## 3.

The Correct Answer is (A) —
We can solve this problem by first simplifying the left side of the equation: 6x-2y-x+5y = 5x+3y. P must equal 5x+3y, so the correct answer choice is A.

## 4.

The Correct Answer is (A) —
We can solve this problem by writing out the relationship as you we read along. Twelve more than three times x, numerically expressed, can be written as 12+3. This equals y, but we must rearrange it to look like our answer choices: 3x+12, which is choice A.

## 10.

The Correct Answer is (6) —
If two thousand people will vote in the first district and one thousand will vote in the second district, then the expression can be written as . Remember that “in thousands of people” means that each number represents one thousand people. The greatest common factor of 6 and 12 is 6.