Simplify: −4(2x+5)
(1 point)
Responses
(−4×2x)+(−4×5)
(−4÷2x)+(−4÷5)
(−4+2x)×(−4+5)
(−4−2x)+(−4−5)
The correct simplification is: (−8x) + (−20)
Put the steps in order for solving the equation: −2(4x+8)+2x = −5x+10
(1 point)
1. Distribute -2 to the terms inside the parentheses: -8x - 16 + 2x = -5x + 10
2. Combine like terms on both sides of the equation: -6x - 16 = -5x + 10
3. Add 5x to both sides of the equation: -6x + 5x - 16 = 10
4. Simplify: -x - 16 = 10
5. Add 16 to both sides of the equation: -x - 16 + 16 = 10 + 16
6. Simplify: -x = 26
7. Multiply both sides of the equation by -1 (to isolate x): (-x)(-1) = 26(-1)
8. Simplify: x = -26
So the solution to the equation is x = -26.
A student solves the following problem: 2(x - 2) + 5x = 24
Step 1: 2x - 4 + 5x = 24
Step 2: 10x - 4 = 24
Step 3: 10x - 4 + 4 = 24 + 4
Step 4: 10x = 28
Step 5: 10x/10=28/10
Step 6: x = 2.8
Where is the mistake? What did the student do incorrectly?
(1 point)
Responses
Step 1: The student should have only distributed the 2 and x, not the x & -2.
Step 3: The student should have subtracted 4 from both sides, not added 4.
Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.
Step 5: The student should have multiplied by 10 on both sides, not divided by 10.
The mistake the student made is: Step 2: The student should have added 2x + 5x = 7x, not (2x)(5) = 10x.
To simplify the expression −4(2x+5), you distribute the -4 to both the terms inside the parentheses.
So, the simplified expression is:
(-4 × 2x) + (-4 × 5)
Simplifying further, you get:
-8x - 20
To simplify the expression −4(2x+5), you can use the distributive property of multiplication over addition.
The distributive property states that the product of a number and a sum is equal to the sum of the products of the number with each term in the sum.
So applying the distributive property to the expression −4(2x+5), you can multiply −4 with each term inside the parentheses:
−4(2x+5) = (−4×2x) + (−4×5)
Simplifying that further gives us:
−8x − 20