Expressions, Equations, and Relationships>Modeling and Solving One-Variable, One-Step Equations and Inequalities(TEKS.Math.6.10.A)
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Texas 6th Grade Math › Expressions, Equations, and Relationships>Modeling and Solving One-Variable, One-Step Equations and Inequalities(TEKS.Math.6.10.A)
The perimeter of a square is 32 cm. What is the side length of the square?
8 cm
4 cm
32 cm
16 cm
Explanation
Let $x$ be the side length. The perimeter of a square is $4x$, so set up $4x = 32$. Divide both sides by 4 to get $x = 8$. Check: $4 \times 8 = 32$, which matches the given perimeter.
Maria needs at least 15 volunteer hours to earn a badge. She already has 8 hours. Let $x$ be the number of additional hours she needs. Which inequality represents this situation?
$x + 15 \ge 8$
$x + 8 \le 15$
$x + 8 \ge 15$
$8 - x \ge 15$
Explanation
Define $x$ as the additional hours. Total hours are $x + 8$, and she needs at least 15, so $x + 8 \ge 15$. Solving gives $x \ge 7$. Check: if she earns 7 more hours, $7 + 8 = 15$, which meets the requirement.
A rectangle has an area of 54 square meters and a width of 6 meters. What is the length?
6 m
8 m
12 m
9 m
Explanation
Let $x$ be the length. Using $A = \ell w$, we have $x \cdot 6 = 54$. Divide both sides by 6 to get $x = 9$. Check: $9 \times 6 = 54$ square meters, which matches the area.
A ride requires a height of at least 48 inches. Sam is 44 inches tall and can add $x$ inches with special shoes. What is the solution for $x$ so Sam can ride?
$x \le 4$
$x \ge 4$
$x \ge 48$
$x \ge -4$
Explanation
Let $x$ be the extra height. The condition is $44 + x \ge 48$. Subtract 44 from both sides: $x \ge 4$. Check: with $x=4$, Sam is $44+4=48$ inches, which meets the requirement.
The temperature increased by 9 degrees to reach 27 degrees. Let $x$ be the starting temperature. Which equation represents this situation?
$x + 9 = 27$
$x - 9 = 27$
$9 - x = 27$
$x + 27 = 9$
Explanation
Starting at $x$ and increasing by 9 to reach 27 is modeled by $x + 9 = 27$. Solving gives $x = 18$. Check: $18 + 9 = 27$, which matches the final temperature.