Question

simplify each expression.

1. $3x + 8x$
2. $8(1 - 3a) - 7$

Explanation:

Problem 32: Simplify \( 3x + 8x \)

Step 1: Identify like terms

Both \( 3x \) and \( 8x \) are like terms (they have the same variable \( x \) raised to the same power, 1).

Step 2: Combine the coefficients

To combine like terms, we add their coefficients. The coefficient of \( 3x \) is 3, and the coefficient of \( 8x \) is 8. So we calculate \( 3 + 8 \).
\( 3 + 8 = 11 \)

Step 3: Write the combined term

After adding the coefficients, we attach the variable \( x \) to the sum of the coefficients. So \( 3x + 8x = 11x \).

Step 1: Distribute the 8

We use the distributive property \( c(a + b) = ca + cb \) (in this case, \( c = 8 \), \( a = 1 \), and \( b = -3a \)) to expand \( 8(1 - 3a) \).
\( 8 \times 1 - 8 \times 3a = 8 - 24a \)

Step 2: Combine like terms

Now we have \( 8 - 24a - 7 \). The constant terms 8 and -7 are like terms. We subtract 7 from 8: \( 8 - 7 = 1 \)

Step 3: Write the simplified expression

Putting it all together, we get \( 1 - 24a \) (or \( -24a + 1 \)).

Answer:

\( 11x \)

Problem 34: Simplify \( 8(1 - 3a) - 7 \)