Question

7)

• x - x - x - x

8)
5(2x - 4) - 3(x - 4)
9)
2x + 4(2x + 1) - 6
10)

• 4(x + 3y) - 2(3x - 5y)

11)
5x + 2y - 2(5x - 4y)
12)
what is the perimeter?
rectangle with sides x, x+3, x, x+3

Explanation:

Problem 7: Simplify \(-x - x - x - x\)

Step 1: Combine like terms

We have four terms of \(-x\), so we add their coefficients. The coefficient of each \(-x\) is \(-1\), so we calculate \(-1 - 1 - 1 - 1\).
\(-1 - 1 - 1 - 1=-4\)
So, \(-x - x - x - x = -4x\)

Problem 8: Simplify \(5(2x - 4)-3(x - 4)\)

Step 1: Distribute the coefficients

First, distribute \(5\) into \((2x - 4)\) and \(-3\) into \((x - 4)\):
\(5(2x - 4)=5\times2x-5\times4 = 10x-20\)
\(-3(x - 4)=-3\times x-3\times(-4)=-3x + 12\)

Step 2: Combine like terms

Now, combine the two resulting expressions:
\((10x-20)+(-3x + 12)=10x-3x-20 + 12\)
\(10x-3x=7x\) and \(-20 + 12=-8\)
So, \(5(2x - 4)-3(x - 4)=7x-8\)

Problem 9: Simplify \(2x + 4(2x + 1)-6\)

Step 1: Distribute the coefficient

Distribute \(4\) into \((2x + 1)\):
\(4(2x + 1)=4\times2x+4\times1 = 8x + 4\)

Step 2: Combine like terms

Now, combine the terms:
\(2x+(8x + 4)-6=2x+8x+4 - 6\)
\(2x+8x = 10x\) and \(4 - 6=-2\)
So, \(2x + 4(2x + 1)-6 = 10x-2\)

Problem 10: Simplify \(-4(x + 3y)-2(3x - 5y)\)

Answer:

s:

1. \(\boldsymbol{-4x}\)
2. \(\boldsymbol{7x - 8}\)
3. \(\boldsymbol{10x - 2}\)
4. \(\boldsymbol{-10x - 2y}\)
5. \(\boldsymbol{-5x + 10y}\)
6. \(\boldsymbol{4x + 6}\)