1. -9x -5 = -95
17
11
10****
-10
2. x/3 -10 = -12
-6***
-66
6
66
3. d/3 + 10 = 7
51
20
0
-9***
4. 2(2 - 2x) = -3x
-4
4***
6
0
5.5.4 + 0.2x =-1.4x + 8.6
2
--2
.2***
20
6.-4 -5(x + 8)
-5x - 44***
-5x + 36
- x - 8
-20x + 8
7. 2x + 3 (x -2) - 3 (x -6)
2x + 12***
2x - 8
8x - 24
2x -24
8. p + 4 < -24
r < -20
r < 28
r < -28***
r < 20
5.5.4 + 0.2x =-1.4x + 8.6
2
--2
.2***
20
========================
1.6 x = 3.2
16 x = 32
x = 2 I get
do #7 more carefully
To solve these equations, we need to isolate the variable on one side of the equation. Here's a step-by-step explanation for each question:
1. -9x - 5 = -95:
- First, we need to isolate the variable term by moving the constant term to the other side of the equation.
- By adding 5 to both sides, we get: -9x = -90.
- Now, we divide both sides by -9 to solve for x: x = -90 / -9.
- Simplifying the expression, we find that x = 10. (Answer: 10)
2. x/3 - 10 = -12:
- To isolate the variable, we start by adding 10 to both sides: x/3 = -2.
- Next, we multiply both sides by 3: 3(x/3) = -2(3).
- Simplifying, we get: x = -6. (Answer: -6)
3. d/3 + 10 = 7:
- Subtracting 10 from both sides of the equation, we have: d/3 = -3.
- To isolate the variable, we multiply both sides by 3: 3(d/3) = -3(3).
- Simplifying gives us: d = -9. (Answer: -9)
4. 2(2 - 2x) = -3x:
- Expanding and simplifying the equation, we have: 4 - 4x = -3x.
- To isolate the variable, we add 4x to both sides: 4 - 4x + 4x = -3x + 4x.
- Simplifying gives us: 4 = x. (Answer: 4)
5. 5.4 + 0.2x =-1.4x + 8.6:
- Firstly, we group like terms together on both sides of the equation: -1.4x + 0.2x = 8.6 - 5.4.
- Simplifying, we have: -1.2x = 3.2.
- Dividing both sides by -1.2, we find: x = 3.2 / -1.2.
- Simplifying the expression, we find x ≈ -2.67. (Answer: -2.67)
6. -4 - 5(x + 8):
- We need to distribute the -5 to both terms inside the parentheses: -4 - 5x - 40.
- Combining like terms, we have: -5x - 44. (Answer: -5x - 44)
7. 2x + 3(x - 2) - 3(x - 6):
- First, we simplify the equation by applying the distributive property: 2x + 3x - 6 - 3x + 18.
- Combining like terms gives us: 2x + 3x - 3x + 12.
- Simplifying further, we have: 2x + 12. (Answer: 2x + 12)
8. p + 4 < -24:
- To isolate the variable, we start by subtracting 4 from both sides: p < -28.
- (Answer: p < -28)