To determine which two expressions are equivalent to the given expression \(4(x + 3) - 10 + 6x\), let's simplify the original expression step-by-step:
-
Distribute the \(4\) into \((x + 3)\): \[ 4(x + 3) = 4x + 12 \]
-
Substitute this back into the expression: \[ 4x + 12 - 10 + 6x \]
-
Combine like terms: \[ 4x + 6x + 12 - 10 = 10x + 2 \]
Now we have simplified the original expression to \(10x + 2\).
Now, let's check which of the provided expressions are equivalent to \(10x + 2\):
- \(-2x - 7\) - Not equivalent.
- \(4x + 3 - 10 + 6x\): \[ 4x + 3 - 10 + 6x = 10x - 7 \quad (\text{Not equivalent.}) \]
- \(4x + 12 - 10 + 6x\): \[ 4x + 12 - 10 + 6x = 10x + 2 \quad (\text{Equivalent!}) \]
- \(2(5x + 1)\): \[ 2(5x + 1) = 10x + 2 \quad (\text{Equivalent!}) \]
- \(10x - 7\) - Not equivalent.
- \(2(8x + 1)\): \[ 2(8x + 1) = 16x + 2 \quad (\text{Not equivalent.}) \]
Thus, the two expressions that are equivalent to the original expression \(4(x + 3) - 10 + 6x\) are:
- \(4x + 12 - 10 + 6x\)
- \(2(5x + 1)\)