Answer:
a) x=-10
b) x = 7
Step-by-step explanation:
These two questions a and b are very similar so let me tell you the steps I would take to solve them.
- Expand the expressions on both sides of the equality sign (=).
- Move constant terms to one side and variable terms to the other.
- Solve equation for x.
So, let's do just that. We start with problem a.
a) [tex]2*(x+3) = x-4[/tex]
1. Expand the expressions
[tex]2*(x+3) = x-4 \implies 2x + 6 = x-4[/tex]
On the LHS we multiplied the terms in the parenthesis by the constant 2.
2. Move constant terms to one side and variable terms to the other.
[tex]2x + 6 = x-4 \implies \\2x + 6 - 6 = x-4-6 \implies \\2x = x-10 \implies \\2x-x = x-10 -x \implies \\x = -10[/tex]
In the second step we subtracted 6 from both sides. In the fourth step we subtracted x from both sides.
3. Solve equation for x
In this example the solution is already given in the last step of part 2.
[tex]x = -10[/tex]
b) [tex]4*(5x-2) = 2*(9x+3)[/tex]
1. Expand the expressions
[tex]4*(5x-2) = 2*(9x+3) \implies 20x-8 = 18x + 6[/tex]
On the LHS we multiplied the terms in the parenthesis by the constant 4.
On the RHS we multiplied the terms in the parenthesis by the constant 2.
2. Move constant terms to one side and variable terms to the other.
[tex]20x-8 = 18x + 6 \implies\\20x-8+8 = 18x + 6 + 8 \implies\\20x = 18x + 14 \implies\\20x - 18x = 18x + 14 - 18x \implies\\2x = 14[/tex]
In the second step we added 8 to both sides. In the fourth step we subtracted 18x from both sides.
3. Solve equation for x
[tex]2x = 14 \implies\\2x / 2 = 14 / 2 \implies\\x = 7[/tex]
In the second step we divided both sides by 2 giving the result x = 7.
