4x-7=x+8
4w-19=w+2
8m-90=75-7m
3(2m-5)=9
4w+2(w-5)
5(2x+8)=6x+32
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x=5, w=7, m=165, m=-1, 6w-10, x=-4
thank you Ejda. this is my first visit to this site so im just figuring this all out. im interested not only in the answers but how to come up with them .I didn't quite understand your first explanation.
4x-7=x+8
move unknowns to one side and numbers to other. Change signs when switching sides.
4x-x = 8+7
combine terms.
3x = 15
divide both sides by 3
3x/3 = 15/3
x = 5
The others are done the same way.
To solve these equations, we can use various algebraic techniques to isolate the variable on one side of the equation. Here's how to solve each equation step by step:
1. 4x - 7 = x + 8
To get rid of the x term on the right side, subtract x from both sides of the equation:
4x - x - 7 = x - x + 8
3x - 7 = 8
To isolate the variable term, add 7 to both sides:
3x - 7 + 7 = 8 + 7
3x = 15
Finally, divide both sides by 3 to solve for x:
3x/3 = 15/3
x = 5
So, the solution to the equation 4x - 7 = x + 8 is x = 5.
2. 4w - 19 = w + 2
To eliminate the w term on the right side, subtract w from both sides:
4w - w - 19 = w - w + 2
3w - 19 = 2
To isolate the variable term, add 19 to both sides:
3w - 19 + 19 = 2 + 19
3w = 21
Finally, divide both sides by 3 to solve for w:
3w/3 = 21/3
w = 7
So, the solution to the equation 4w - 19 = w + 2 is w = 7.
3. 8m - 90 = 75 - 7m
To eliminate the -7m term on the right side, add 7m to both sides:
8m - 90 + 7m = 75 - 7m + 7m
15m - 90 = 75
To isolate the variable term, add 90 to both sides:
15m - 90 + 90 = 75 + 90
15m = 165
Finally, divide both sides by 15 to solve for m:
15m/15 = 165/15
m = 11
So, the solution to the equation 8m - 90 = 75 - 7m is m = 11.
4. 3(2m - 5) = 9
To solve this equation, first distribute the 3 to both terms inside the parentheses:
3 * 2m - 3 * 5 = 9
6m - 15 = 9
To isolate the variable term, add 15 to both sides:
6m - 15 + 15 = 9 + 15
6m = 24
Finally, divide both sides by 6 to solve for m:
6m/6 = 24/6
m = 4
So, the solution to the equation 3(2m - 5) = 9 is m = 4.
5. 4w + 2(w - 5)
To solve this equation, first distribute the 2 to both terms inside the parentheses:
4w + 2w - 2 * 5
Combine like terms:
6w - 10
So, the simplified form of 4w + 2(w - 5) is 6w - 10.
6. 5(2x + 8) = 6x + 32
To solve this equation, first distribute the 5 to both terms inside the parentheses:
5 * 2x + 5 * 8 = 6x + 32
10x + 40 = 6x + 32
To isolate the x term, subtract 6x from both sides:
10x - 6x + 40 = 6x - 6x + 32
4x + 40 = 32
To isolate the variable term, subtract 40 from both sides:
4x + 40 - 40 = 32 - 40
4x = -8
Finally, divide both sides by 4 to solve for x:
4x/4 = -8/4
x = -2
So, the solution to the equation 5(2x + 8) = 6x + 32 is x = -2.