10 a. 7m + 36 =11m b. 2x+ 4=10x-4 c.11w-8=22-w d.6a - 12-a = 9a +53+a
a)
7m + 36 = 11m
-4m = -36
m = 9
b)
2x + 4 = 10x - 4
-8x = -8
x = 1
c)
11w - 8 = 22 - w
12w = 30
w = 5/2
d)
6a - 12 - a = 9a + 53 + a
5a - 12 = 10a + 53
-5a = 65
a = -13
To solve these equations, we need to isolate the variable on one side of the equation. Let's go through each equation step by step:
a) 7m + 36 = 11m
To solve for m:
1. Start by subtracting 7m from both sides of the equation to isolate the variable term:
7m - 7m + 36 = 11m - 7m
36 = 4m
2. Next, divide both sides of the equation by 4 to solve for m:
36/4 = 4m/4
9 = m
So the solution is m = 9.
b) 2x + 4 = 10x - 4
To solve for x:
1. Start by subtracting 2x from both sides of the equation to isolate the variable term:
2x - 2x + 4 = 10x - 2x - 4
4 = 8x - 4
2. Next, add 4 to both sides of the equation to isolate the constant term:
4 + 4 = 8x - 4 + 4
8 = 8x
3. Now, divide both sides of the equation by 8 to solve for x:
8/8 = 8x/8
1 = x
So the solution is x = 1.
c) 11w - 8 = 22 - w
To solve for w:
1. Start by adding w to both sides of the equation to move all variable terms to one side:
11w + w - 8 = 22 - w + w
12w - 8 = 22
2. Next, add 8 to both sides of the equation to isolate the variable term:
12w - 8 + 8 = 22 + 8
12w = 30
3. Now, divide both sides of the equation by 12 to solve for w:
12w/12 = 30/12
w = 2.5
So the solution is w = 2.5.
d) 6a - 12 - a = 9a + 53 + a
To solve for a:
1. Combine like terms on both sides of the equation:
6a - a - 12 = 9a + a + 53
5a - 12 = 10a + 53
2. Next, subtract 10a from both sides of the equation to isolate the variable term:
5a - 10a - 12 = 10a - 10a + 53
-5a - 12 = 53
3. Now, add 12 to both sides of the equation to isolate the constant term:
-5a - 12 + 12 = 53 + 12
-5a = 65
4. Finally, divide both sides of the equation by -5 to solve for a:
-5a/-5 = 65/-5
a = -13
So the solution is a = -13.