Expressions, Equations, and Relationships>Determining if Values Satisfy Two-Step Equations or Inequalities(TEKS.Math.7.11.B)
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Texas 7th Grade Math › Expressions, Equations, and Relationships>Determining if Values Satisfy Two-Step Equations or Inequalities(TEKS.Math.7.11.B)
Which value(s) make this equation true? Test $x = 4$, $x = 5$, $x = 3$ in $3x - 5 = 7$.
$x = 4$ only
$x = 5$ only
$x = 3$ only
$x = 4$ and $x = 5$
Explanation
Test $x=4$: $3(4)-5=12-5=7$, which equals $7$ (true). Test $x=5$: $3(5)-5=15-5=10$, which is not $7$ (false). Test $x=3$: $3(3)-5=9-5=4$, which is not $7$ (false). Therefore, only $x=4$ makes the equation true.
Test these solutions in the inequality $2y + 8 < 20$: $y = 3$, $y = 5$, $y = 7$. Which are true?
$y = 3$ only
$y = 5$ only
$y = 3$ and $y = 5$
$y = 3$, $y = 5$, and $y = 7$
Explanation
Test $y=3$: $2(3)+8=6+8=14<20$ (true). Test $y=5$: $2(5)+8=10+8=18<20$ (true). Test $y=7$: $2(7)+8=14+8=22<20$ (false). So $y=3$ and $y=5$ satisfy the inequality.
Which value(s) satisfy the inequality $\tfrac{1}{2}x - 7 \ge -1$? Test $x = 10$, $x = 12$, $x = 14$.
$x = 10$ only
$x = 12$ only
$x = 10$ and $x = 12$
$x = 12$ and $x = 14$
Explanation
Test $x=10$: $\tfrac{1}{2}(10)-7=5-7=-2\ge -1$? (false). Test $x=12$: $\tfrac{1}{2}(12)-7=6-7=-1\ge -1$ (true). Test $x=14$: $\tfrac{1}{2}(14)-7=7-7=0\ge -1$ (true). Therefore, $x=12$ and $x=14$ satisfy the inequality.
Test these solutions in the equation $-2z + 9 = 1$: $z = 3$, $z = 4$, $z = 5$. Which are true?
$z = 3$ only
$z = 4$ only
$z = 5$ only
$z = 3$ and $z = 5$
Explanation
Test $z=3$: $-2(3)+9=-6+9=3$, not $1$ (false). Test $z=4$: $-2(4)+9=-8+9=1$ (true). Test $z=5$: $-2(5)+9=-10+9=-1$, not $1$ (false). So only $z=4$ makes the equation true.
Which value(s) make the inequality $-3k + 6 \le 0$ true? Test $k = 2$, $k = 3$, $k = 4$.
$k = 2$ only
$k = 2$, $k = 3$, and $k = 4$
$k = 3$ and $k = 4$ only
$k = 2$ and $k = 4$ only
Explanation
Test $k=2$: $-3(2)+6=-6+6=0\le 0$ (true). Test $k=3$: $-3(3)+6=-9+6=-3\le 0$ (true). Test $k=4$: $-3(4)+6=-12+6=-6\le 0$ (true). All three values satisfy the inequality.