Solve the Equations
142=58-7x
2x+96=-44-3x
-26=-7x+4(2x-4)
7x+5(-4x-4)=-124
-7x-35=28
10x+36=-108-2x
1. 7x = 58-142 = -84
X = -12.
2. 5x = -44-96 = -140
X = -28.
3. -26 = -7x+8x-16
-26 = x-16
x = 16-26 = -10
4. Similar to #3.
5. Similar to #1.
6.
To solve the equations, we will follow a step-by-step process to isolate the variable (x) and find its value.
1. 142 = 58 - 7x
To isolate the term with x, we will move the constant terms (numbers without x) to one side of the equation and the term with x to the other side.
→ 142 + 7x = 58
Now we will simplify the equation by combining like terms. Add 7x to both sides.
→ 142 + 7x + (-7x) = 58 + (-7x)
Simplifying further:
→ 142 = 58 + (-7x)
Next, we will move the constant term of 58 to the left side of the equation by subtracting it from both sides.
→ 142 - 58 = 58 + (-7x) - 58
Simplifying the equation:
→ 84 = -7x
Finally, to solve for x, we will divide both sides of the equation by -7.
→ 84 / -7 = -7x / -7
→ x = -12
Therefore, the solution to the equation is x = -12.
2. 2x + 96 = -44 - 3x
Following the same process, let's isolate the term with x.
→ 2x + 3x = -44 - 96
Combine like terms:
→ 5x = -140
To solve for x, divide both sides of the equation by 5:
→ 5x / 5 = -140 / 5
→ x = -28
So, the value of x is -28.
3. -26 = -7x + 4(2x - 4)
Start by simplifying the equation within parentheses:
→ -26 = -7x + 4(2x) + 4(-4)
→ -26 = -7x + 8x - 16
Combine like terms:
→ -26 = x - 16
Move the constant term -16 to the left side:
→ -26 + 16 = x
Simplify:
→ -10 = x
Therefore, x = -10.
4. 7x + 5(-4x - 4) = -124
To simplify the equation, distribute the 5 to both terms inside the parentheses:
→ 7x - 20x - 20 = -124
Combine like terms:
→ -13x - 20 = -124
Move the constant term -20 to the right side:
→ -13x = -124 + 20
Simplify:
→ -13x = -104
To solve for x, divide both sides of the equation by -13:
→ -13x / -13 = -104 / -13
→ x = 8
Therefore, the solution is x = 8.
5. -7x - 35 = 28
To solve for x, isolate the term with x by moving the constant term -35 to the right side:
→ -7x = 28 + 35
Simplify:
→ -7x = 63
Divide both sides of the equation by -7 to solve for x:
→ -7x / -7 = 63 / -7
→ x = -9
The solution is x = -9.
6. 10x + 36 = -108 - 2x
First, add 2x to both sides to isolate the term with x:
→ 10x + 2x + 36 = -108
Combine like terms:
→ 12x + 36 = -108
Next, move the constant term 36 to the right side of the equation:
→ 12x = -108 - 36
Simplify:
→ 12x = -144
Divide both sides of the equation by 12:
→ 12x / 12 = -144 / 12
→ x = -12
Therefore, the solution is x = -12.