Equation Equilibrium Worksheet
Name:
Date:
Period:
Equation Equilibrium
Directions: Solve for the unknown variable.
1 \( 4 + 3(2m - 5) = 7 - 2(m - 3) \)
Solution: m =
2 \( 9 - 4(k + 2) = 3(2k - 1) - 4 \)
Solution: k =
3 \( -2(3w - 1) - 8 = -6 + 4(w + 5) \)
Solution: w =
4 \( 8 - 3(2p + 1) = 5 + 2(3p - 4) \)
Solution: p =
STAAR Equation Solving Practice Sheet
Name:
Date:
Period:
Linear Equation Application
TEKS A.5(A) • Algebra 1 STAAR
Directions: Write an equation for each situation and solve for the variable.
1
A rectangular garden and an equilateral triangular enclosure have identical perimeters. The dimensions are shown below in meters. Construct an equation and solve to determine the value of \( w \).
\( 2(w + 4) \)
\( 3 \)
Rectangle
\( 3(w - 1) + 2 \) Equilateral Triangle
A \( w = 5 \)
B \( w = \frac{23}{5} \)
C \( w = 8 \)
D \( w = \frac{17}{5} \)
2
Two catering companies determine their total charge in dollars for an event based on \( m \) hours of service:
Chef Express \( \$60 \) equipment fee plus \( \$30 \) per hour for \( (m + 2) \) hours, minus a \( \$10 \) promotional discount.
Gourmet Delight \( \$25 \) setup fee plus \( \$20 \) per hour for \( (2m - 1) \) hours, plus an additional \( \$40 \) cleanup fee.
For what value of \( m \) will the total charges of both catering companies be equal?
A \( m = 5 \)
B \( m = \frac{13}{2} \)
C \( m = \frac{9}{2} \)
D \( m = 7 \)
3
The area of the rectangle shown below is \( 10 \) square centimeters greater than the area of the right triangle. Write an equation modeling this relationship and solve for \( p \).
\( 2p - 1 \)
\( 6 \)
Rectangle
\( p + 4 \)
\( \text{Base} = 8 \) Right Triangle
A \( p = \frac{11}{4} \)
B \( p = 6 \)
C \( p = 4 \)
D \( p = \frac{15}{2} \)
Name:
Date:
Period:
Linear Equation Application
TEKS A.5(A) • Page 2
Directions: Write an equation for each situation and solve for the variable.
4
Two liquid storage tanks are being monitored in a laboratory experiment over \( t \) minutes:
- Tank A: Holds \( 25 \) liters initially, then receives inflow at \( 3(4t - 1) \) liters plus a \( 8 \)-liter buffer.
- Tank B: Holds \( 85 \) liters initially, but drains at \( 2(3t + 2) \) liters with an additional \( 6 \)-liter loss.
Construct a linear equation representing when both tanks hold an equal volume of liquid, and solve for \( t \).
A \( t = 3 \)
B \( t = \frac{5}{2} \)
C \( t = \frac{7}{2} \)
D \( t = 2 \)
5
Two student clubs are raising funds over \( k \) school weeks:
Beta Club Starts with \( \$30 \), earns \( \$4 \) per item on \( (3k - 2) \) items sold, and receives a \( \$5 \) alumni gift.
Robotics Club Starts with \( \$63 \), earns \( \$2 \) per ticket on \( (k + 4) \) tickets, and receives a \( \$6 \) sponsor bonus.
After how many weeks, \( k \), will both clubs have accumulated the exact same total amount?
A \( k = 4 \)
B \( k = \frac{11}{2} \)
C \( k = 7 \)
D \( k = 5 \)
6
A regular hexagon has sides measuring \( [2(r - 1) + 3] \) cm. A rectangle has length \( 3(3r + 1) \) cm and width \( 4 \) cm. The perimeter of the hexagon is \( 16 \) cm less than the perimeter of the rectangle. What is the value of \( r \)?
\( 2(r - 1) + 3 \) Regular Hexagon
\( 3(3r + 1) \)
\( 4 \)
Rectangle
A \( r = 2 \)
B \( r = \frac{4}{3} \)
C \( r = \frac{5}{3} \)
D \( r = 1 \)
