Question

do you know how?
in 6–15, simplify each expression.

1. ( x + x + x + x )
2. ( 4y - y )
3. ( 7y - 4.5 - 6y )
4. ( 4x + 2 - \frac{1}{2}x )
5. ( 3 + 3y - 1 + y )
6. ( x + 6x )
7. ( 0.5w + 1.7w - 0.5 )
8. ( 12\frac{1}{3}b + 6\frac{2}{3} - 10\frac{2}{3}b )
9. ( \frac{3}{4}x + 2 + 3x - \frac{1}{2} )
10. ( 3.2x + 6.5 - 2.4x - 4.4 )

Explanation:

Let's solve each problem one by one:

Problem 6: \( x + x + x + x \)

Step 1: Combine like terms

There are 4 \( x \) terms. So we add their coefficients. The coefficient of each \( x \) is 1. So \( 1x + 1x + 1x + 1x=(1 + 1+1 + 1)x \)

Step 2: Calculate the sum of coefficients

\( 1+1 + 1+1 = 4 \), so the simplified expression is \( 4x \)

Step 1: Combine like terms

The coefficients of \( y \) are 4 and - 1 (since \( y=1y \), so \( -y=- 1y \)). So we have \( (4-1)y \)

Step 2: Calculate the difference of coefficients

\( 4 - 1=3 \), so the simplified expression is \( 3y \)

Step 1: Combine like terms (the \( y \) terms)

\( 7y-6y=(7 - 6)y \)

Step 2: Calculate the difference of coefficients for \( y \) terms

\( 7-6 = 1 \), so \( 7y-6y=y \). Then the expression becomes \( y-4.5 \)

Answer:

\( 4x \)

Problem 7: \( 4y - y \)