Question

part ii – constructed response
solve each equation.

1. 7.3 = y + 2.8
2. $2 = -5 + \frac{y}{4}$
3. $6m - 10m = 36$
4. $8d + 6 = 5d + 39$

solve each equation. circle the number of solutions (one, none or infinitely many).

1. $3x + 1 = 3x + 4$
2. $4(x + 3) = 4x + 12$

one one
none none
infinitely many infinitely many

Explanation:

1. Solve \( 7.3 = y + 2.8 \)

Step1: Subtract 2.8 from both sides

To isolate \( y \), we subtract 2.8 from both sides of the equation.
\( 7.3 - 2.8 = y + 2.8 - 2.8 \)

Step2: Simplify both sides

Calculate the left - hand side: \( 7.3-2.8 = 4.5 \), and the right - hand side simplifies to \( y \) (since \( y + 2.8-2.8=y\)).

Step1: Add 5 to both sides

To isolate the term with \( v \), we add 5 to both sides of the equation.
\( 2 + 5=-5+\frac{v}{4}+5 \)

Step2: Simplify both sides

The left - hand side: \( 2 + 5=7 \), the right - hand side simplifies to \( \frac{v}{4} \) (since \( - 5+5 = 0\)).

Step3: Multiply both sides by 4

To solve for \( v \), multiply both sides of the equation \( 7=\frac{v}{4} \) by 4.
\( 7\times4=\frac{v}{4}\times4 \)

Step4: Simplify both sides

The left - hand side: \( 7\times4 = 28 \), the right - hand side simplifies to \( v \) (since \( \frac{v}{4}\times4=v\)).

Step1: Combine like terms

Combine the terms with \( m \) on the left - hand side. \( 6m-10m=(6 - 10)m=-4m \)
So the equation becomes \( - 4m=36 \)

Step2: Divide both sides by - 4

To solve for \( m \), divide both sides of the equation \( -4m = 36 \) by - 4.
\( m=\frac{36}{-4} \)

Step3: Simplify the fraction

\( \frac{36}{-4}=-9 \)

Answer:

\( y = 4.5 \)

2. Solve \( 2=-5+\frac{v}{4} \)