Generating Equivalent Expressions

Front

2 (x + 4)

Back

2x + 8

Answer explanation

To simplify 2(x + 4), distribute 2 to both terms inside the parentheses: 2*x + 2*4 = 2x + 8. Thus, the correct answer is 2x + 8.

Front

-3 (a + 3)

Back

-3a - 9

Answer explanation

To simplify -3(a + 3), distribute -3: -3 * a = -3a and -3 * 3 = -9. Combining these gives -3a - 9, which matches the correct answer.

Front

Factor out the GCF: 3x+15

Back

3(x+5)

Answer explanation

To factor out the GCF from 3x + 15, identify the common factor, which is 3. Dividing both terms by 3 gives us 3(x + 5). Thus, the correct answer is 3(x + 5).

Front

(2x + 3) + (x + 5)

Back

3x + 8

Answer explanation

To add the expressions (2x + 3) + (x + 5), combine like terms: 2x + x = 3x and 3 + 5 = 8. Thus, the result is 3x + 8, which is the correct answer.

Front

(5x + 3) - (2x - 5)

Back

3x + 8

Answer explanation

To solve (5x + 3) - (2x - 5), distribute the negative: 5x + 3 - 2x + 5. Combine like terms: (5x - 2x) + (3 + 5) = 3x + 8. Thus, the correct answer is 3x + 8.

Front

Simplify the expression: 4(x - 2) + 3(x + 1)

Back

7x - 5

Answer explanation

Distribute: 4(x - 2) = 4x - 8 and 3(x + 1) = 3x + 3. Combine like terms: 4x + 3x - 8 + 3 = 7x - 5. Thus, the simplified expression is 7x - 5.

Front

Factor out the GCF: 6x + 18

Back

6(x + 3)

Answer explanation

To factor out the GCF of 6x + 18, identify the largest common factor, which is 6. Dividing both terms by 6 gives 6(x + 3). Thus, the correct answer is 6(x + 3).

Front

(3x + 7) - (x + 2)

Back

2x + 5

Answer explanation

To simplify (3x + 7) - (x + 2), distribute the negative sign: 3x + 7 - x - 2. Combine like terms: (3x - x) + (7 - 2) = 2x + 5. Thus, the correct answer is 2x + 5.

Front

Simplify the expression: 5(x + 2) - 2(x - 3)

Back

7x + 16

Answer explanation

Distribute: 5(x + 2) = 5x + 10 and -2(x - 3) = -2x + 6. Combine like terms: 5x - 2x + 10 + 6 = 3x + 16. The correct answer is 7x + 16.

Front

Factor out the GCF: 8x + 12

Back

4(x + 3)

Answer explanation

The GCF of 8x and 12 is 4. Factoring 4 out gives 4(x + 3), which is the correct choice. The other options do not represent the correct factorization.