Put the steps in order for solving the equation: −2(4x+8)+2x = −5x+10
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1. Start by distributing the -2 on the left side of the equation: -8x - 16 + 2x = -5x + 10
2. Combine like terms on both sides: -8x + 2x - 16 = -5x + 10
3. Simplify the equation: -6x - 16 = -5x + 10
4. Move all the x terms to one side of the equation: -6x + 5x = 10 + 16
5. Combine like terms on both sides: -x = 26
6. Divide both sides of the equation by -1 to solve for x: 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?
The mistake is in Step 3. The student incorrectly added 4 to both sides of the equation instead of subtracting 4 from both sides.
The correct step 3 should be: 10x - 4 - 4 = 24 - 4
This would result in: 10x - 8 = 20
To solve the equation: 24(34+x)=1,200
, give the reasons for each of the given steps.
What was done to the previous step to get to the current equation?
Step 1: 816+24x=1,200
Step 2: 816−816+24x=1,200 − 816
Step 3: 24x=384
Step 4: x=1
Step 1: 816+24x=1,200
To get to step 1, the equation was simplified by distributing 24 to both terms inside the parentheses.
Step 2: 816−816+24x=1,200 − 816
To get to step 2, 816 was subtracted from both sides of the equation in order to isolate the term with 24x.
Step 3: 24x=384
To get to step 3, the terms on the left side of the equation were combined by subtracting 816 from 816, resulting in 0.
Step 4: x=1
To get to step 4, both sides of the equation were simplified by dividing by 24 to solve for x.
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Question
To solve the equation: 24(34+x)=1,200
, give the reasons for each of the given steps.
What was done to the previous step to get to the current equation?
.
Step 1: 816+24x=1,200
Step 2: 816−816+24x=1,200 − 816
Step 3: 24x=384
Step 4: x=16
Step 1: 816+24x=1,200
To get to step 1, the equation was simplified by multiplying 24 with 34+x.
Step 2: 816−816+24x=1,200 − 816
To get to step 2, 816 was subtracted from both sides of the equation in order to isolate the term with 24x.
Step 3: 24x=384
To get to step 3, the terms on the left side of the equation were combined by subtracting 816 from 816, resulting in 0.
Step 4: x=16
To get to step 4, both sides of the equation were simplified by dividing by 24 to solve for x.
Simplify: −4(2x+5)
(−4−2x)+(−4−5)
(−4+2x)×(−4+5)
(−4×2x)+(−4×5)
(−4÷2x)+(−4÷5
−4(2x + 5) simplifies to -8x - 20.
(−4−2x) + (−4−5) simplifies to -8 - 2x - 9 which further simplifies to -17 - 2x.
(−4+2x) × (−4+5) simplifies to (-4 + 2x) × 1 which further simplifies to -4 + 2x.
(−4 × 2x) + (−4 × 5) simplifies to -8x - 20.
(−4 ÷ 2x) + (−4 ÷ 5) does not simplify as it involves division of variables.
To solve the equation −2(4x+8)+2x = −5x+10, follow these steps:
Step 1: Distribute the -2 to the terms inside the parentheses:
-2 * 4x = -8x
-2 * 8 = -16
The equation becomes:
-8x - 16 + 2x = -5x + 10
Step 2: Combine like terms on both sides of the equation:
(-8x + 2x) - 16 = -5x + 10
-6x - 16 = -5x + 10
Step 3: Move all terms containing x to one side of the equation:
-6x + 5x - 16 = 10
-x - 16 = 10
Step 4: Add 16 to both sides of the equation to isolate the term with x:
-x - 16 + 16 = 10 + 16
-x = 26
Step 5: Multiply the entire equation by -1 to get x positive:
x = -26
Therefore, the solution to the equation is x = -26.