Answer:
1) x= 7
2)a. x=8, x=1
b.x=4,x=-1
3)(5,2)
Step-by-step explanation:
problem 1:
1) Distribute
4(x-5)=x+1
4x-20=x+1
2) Add 20 to both sides of the equation
4x-20=x+1
4x-20+20=x+1+20
3) Simplify
*Add the numbers
4x=x+21
4) Subtract x from both sides of the equation
4x=x+21
4x-x=x+21-x
5) Simplify
*Combine like terms
3x=21
6) Divide both sides of the equation by the same term.
3x=21
3x/3=21/3
7) Simplify
*Cancel terms that are in both the numerator and denominator
*Divide the numbers
Result: x=7
-------------------------------------
problem 2:
a
1) Use the sum-product pattern
Identify a, b, and c in your equation and then find two numbers that when multiplied together equal c and when added together equal b.
x²-9x+8=0
2) Factor
* Write your equation in factored form
(x-8)(x-1)=0
3) Create two separate equations
*set each factor equal to 0
x-8=0
x-1=0
4) solve
*rearrange and isolate the variable to find each solution
x=8
x=1
b.
1) move terms to the left side
2x²+7x-4=x²+10x
2x²+7x-4-(x²+10x)=0
2) distribute
2x²+7x-4=x²+10x
2x²+7x-4-x²-10x=0
3) combine like terms
2x²+7x-4-x²-10x=0
1x²+7x-4-10x=0
4) Multiply by 1
1x²+7x-4-10x=0
x²+7x-4-10x=0
5) combine like terms
x²+7x-4-10x=0
x²-3x-4=0
6) Use the sum-product pattern
Identify a, b, and c in your equation and then find two numbers that when multiplied together equal c and when added together equal b.
x²-3x-4-0
7) Factor
Write your equation in factored form
(x-4)(x+1)=0
8) Create two separate equations
Set each factor equal to zero
x-4=0
x+1=0
9) Solve
Rearrange and isolate the variable to find each solution
x=4
x= -1
-=----------------------
problem 3:
x+4y=13
x-y-3
multiplying this one by -1
x+4y=13
-x+y=-3
0x+5y=10
5y=10
y=10/2
y=2
since we know that
x-y=3
x-(2)=3
x=5
(5,2)
110
