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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

Study concepts, example questions & explanations for Common Core: High School - Algebra

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All Common Core: High School - Algebra Resources

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Example Questions

Example Question #301 : Reasoning With Equations & Inequalities

Is the point $\left(34,-28\right)$ $\displaystyle \left(34,-28\right)$ included in the inequality $y\geq- 26 x^{3}$ $\displaystyle y\geq- 26 x^{3}$ ?

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ $\displaystyle \uptext{x}$ value. $-28\geq-26\cdot34^{3}$ $\displaystyle -28\geq-26\cdot34^{3}$ $-28\geq-26\cdot39304$ $\displaystyle -28\geq-26\cdot39304$ $-28\geq-1021904$ $\displaystyle -28\geq-1021904$

Since $\displaystyle -28$is greater than$\displaystyle -1021904$the point is included in the inequality.

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Example Question #302 : Reasoning With Equations & Inequalities

Is the point $\left(47,-18\right)$ $\displaystyle \left(47,-18\right)$ included in the inequality $y\geq- 7 x^{5}$ $\displaystyle y\geq- 7 x^{5}$ ?

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ $\displaystyle \uptext{x}$ value. $-18\geq-7\cdot47^{5}$ $\displaystyle -18\geq-7\cdot47^{5}$ $-18\geq-7\cdot229345007$ $\displaystyle -18\geq-7\cdot229345007$ $-18\geq-1605415049$ $\displaystyle -18\geq-1605415049$

Since $\displaystyle -18$is greater than$\displaystyle -1605415049$the point is included in the inequality.

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Example Question #303 : Reasoning With Equations & Inequalities

Is the point $\left(35,-32\right)$ $\displaystyle \left(35,-32\right)$ included in the inequality $y\geq- 32 x^{2}$ $\displaystyle y\geq- 32 x^{2}$ ?

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ $\displaystyle \uptext{x}$ value. $-32\geq-32\cdot35^{2}$ $\displaystyle -32\geq-32\cdot35^{2}$ $-32\geq-32\cdot1225$ $\displaystyle -32\geq-32\cdot1225$ $-32\geq-39200$ $\displaystyle -32\geq-39200$

Since $\displaystyle -32$is greater than$\displaystyle -39200$the point is included in the inequality.

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Example Question #304 : Reasoning With Equations & Inequalities

Is the point $\left(32,-39\right)$ $\displaystyle \left(32,-39\right)$ included in the inequality $y\geq- 25 x^{4}$ $\displaystyle y\geq- 25 x^{4}$ ?

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ $\displaystyle \uptext{x}$ value. $-39\geq-25\cdot32^{4}$ $\displaystyle -39\geq-25\cdot32^{4}$ $-39\geq-25\cdot1048576$ $\displaystyle -39\geq-25\cdot1048576$ $-39\geq-26214400$ $\displaystyle -39\geq-26214400$

Since $\displaystyle -39$is greater than$\displaystyle -26214400$the point is included in the inequality.

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Example Question #305 : Reasoning With Equations & Inequalities

Is the point $\left(13,3\right)$ $\displaystyle \left(13,3\right)$ included in the inequality $y\geq- 21 x^{2}$ $\displaystyle y\geq- 21 x^{2}$ ?

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ $\displaystyle \uptext{x}$ value. $3\geq-21\cdot13^{2}$ $\displaystyle 3\geq-21\cdot13^{2}$ $3\geq-21\cdot169$ $\displaystyle 3\geq-21\cdot169$ $3\geq-3549$ $\displaystyle 3\geq-3549$

Since $\displaystyle 3$is greater than$\displaystyle -3549$the point is included in the inequality.

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Example Question #306 : Reasoning With Equations & Inequalities

Is the point $\left(42,-47\right)$ $\displaystyle \left(42,-47\right)$ included in the inequality $y\geq- 26 x^{4}$ $\displaystyle y\geq- 26 x^{4}$ ?

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ $\displaystyle \uptext{x}$ value. $-47\geq-26\cdot42^{4}$ $\displaystyle -47\geq-26\cdot42^{4}$ $-47\geq-26\cdot3111696$ $\displaystyle -47\geq-26\cdot3111696$ $-47\geq-80904096$ $\displaystyle -47\geq-80904096$

Since $\displaystyle -47$is greater than$\displaystyle -80904096$the point is included in the inequality.

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Example Question #307 : Reasoning With Equations & Inequalities

Is the point $\left(4,-26\right)$ $\displaystyle \left(4,-26\right)$ included in the inequality $y\geq- 4 x^{5}$ $\displaystyle y\geq- 4 x^{5}$ ?

Possible Answers:

Yes

Correct answer:

Yes

Explanation:

To see if the point is included in the inequality, we need to plug in the $\uptext{x}$ $\displaystyle \uptext{x}$ value. $-26\geq-4\cdot4^{5}$ $\displaystyle -26\geq-4\cdot4^{5}$ $-26\geq-4\cdot1024$ $\displaystyle -26\geq-4\cdot1024$ $-26\geq-4096$ $\displaystyle -26\geq-4096$

Since $\displaystyle -26$is greater than$\displaystyle -4096$the point is included in the inequality.

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All Common Core: High School - Algebra Resources

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Common Core: High School - Algebra : Reasoning with Equations & Inequalities

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #301 : Reasoning With Equations & Inequalities

Example Question #302 : Reasoning With Equations & Inequalities

Example Question #303 : Reasoning With Equations & Inequalities

Example Question #304 : Reasoning With Equations & Inequalities

Example Question #305 : Reasoning With Equations & Inequalities

Example Question #306 : Reasoning With Equations & Inequalities

Example Question #307 : Reasoning With Equations & Inequalities

All Common Core: High School - Algebra Resources

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