Answer:
Below in bold.
Step-by-step explanation:
I'll solve a few of them to illustrate the method:
a) 5x - (3x - 1) = x - 4
The aim is to get all the 'x' terms to one sides of the '=' and the numbers to the other side:
Distribute the negative over the 3x - 1 in the parentheses:
5x - 3x + 1 = x - 4 ( Note that -* -1 = + 1)
Now subtract 1 from both sides:
5x - 3x + 1 - 1 = x - 4 - 1
5x - 3x = x - 5
Now subtract x from both sides:
5x - 3x - x = x - x - 5.
2x - x = -5
x = -5.
(b) 3/5 x + 1 = 2/5 - 3x
We first get rid of the fractions by multiplying each term by 5:
5 * 3/5 x + 1*5 = 5 * 2/5 - 5*3x
3x + 5 = 2 - 15x
3x + 15x + 5 = 2 - 15x + 15x (adding 15x to both sides)
18x + 5 = 2 Subtract 5 from both sides:
18x + 5 - 5 = 2 - 5
18x = -3
Now we divide both sides by 18:
x = -3/18 = -1/6.
g) 0.3(6 + m) = 0.4(8 - m)
0.3 * 6 + 0.3* m = 0.4*8 + 0.4 * -m ( Distributing the 0.3 and 0.4 over the parentheses)
1.8 + 0.3m = 3.2 - 0.4m ( recall that + * - = -)
1.8 - 1.8 + 0.3m = 3.2 - 1.8 - 0.4m
0.3m = 1.4 - 0.4m
0.3m + 0.4m = 1.4 - 0.4m + 0.4m
0.7m = 1.4
m = 1/4/0.7
m = 2.
I hope this helps.
