Find the value of this integer expression:
2( + 3 + − 4 + − 8 + + 7)
I need to know how to do it with distribution and without distribution
HELP PLX NEED HELP
with: 2(+3) + 2(− 4) + 2(− 8) + 2(+7)
without: 2(-2)
thanks steve
To find the value of the integer expression 2( + 3 + − 4 + − 8 + + 7), let's break it down step-by-step.
With Distribution:
To simplify the expression using distribution, we multiply the coefficient 2 to every term inside the parentheses.
2( + 3 + − 4 + − 8 + + 7) becomes:
2 × + 2 × 3 + 2 × (− 4) + 2 × (− 8) + 2 × 7
Simplifying further, we have:
2 + 6 + (−8) + (−16) + 14
Adding all the terms together:
2 + 6 − 8 − 16 + 14 = −2
So, the value of the expression is −2.
Without Distribution:
To simplify the expression without using distribution, we can combine terms of the same sign.
2( + 3 + − 4 + − 8 + + 7) can be rewritten as:
2 − 4 − 8 + 3 + 7
Adding all the terms together:
2 − 4 − 8 + 3 + 7 = 0
Therefore, the value of the expression is 0.
To find the value of the integer expression 2( + 3 + − 4 + − 8 + + 7), we can solve it using both distribution and without distribution.
1. Solving with Distribution:
First, let's distribute the 2 to every term inside the parentheses:
2 × + 2 × 3 + 2 × − 4 + 2 × − 8 + 2 × 7
Simplifying this equation, we have:
2 × + 6 + − 8 + − 16 + 14
Now, we can combine like terms:
2 + 6 − 8 − 16 + 14 = −2
Therefore, the value of the expression, using distribution, is −2.
2. Solving without Distribution:
If you prefer to solve the expression without using distribution, follow these steps:
Step 1: Group the terms with the same sign and perform the operations from left to right.
Group 1: + 3
Group 2: − 4
Group 3: − 8
Group 4: + 7
Step 2: Add or subtract the terms within each group:
Group 1: 0 + 3 = 3
Group 2: 3 − 4 = −1
Group 3: −1 − 8 = −9
Group 4: −9 + 7 = −2
So, without distribution, the value of the expression is also −2.
In both cases, the answer is −2.