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Published byEmory Wilkins Modified over 8 years ago

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2 step inequalities notes Absent copy Mon 4/22,23

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Inequality Clues x 3 = x is greater than 3 Graph = x 3 = x is greater than or equal to 3 Graph =

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Example 1 Solve and graph 2x + 7 < 17 -7 -7 0 10 2x < 10 2 2 x < 5 -5 0 5 Solution What inverse do we use first? We use the inverse of addition and subtract 7 from both sides. What is the next inverse that we use? We use the inverse of mult. and div. 2 on both sides. What type of circle do we use on the # line? OPEN or CLOSED Which way does the graphed line point? The line points to the left the same way the arrow faces. (…0,1,2,3,4)

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Example 2 Solve and Graph 22 > -11 + 3y +11 +11 33 0 33 > 3y 3 3 y < 11 -11 0 11 Solution What inverse do we use first? We use the inverse of subtraction and add 11 to both sides. What inverse do we use next? We use the inverse of mult. and div. 3 on both sides. What is the proper way to write the solution? We write the solution with the variable in the front. What type of circle do we use on the # line? OPEN or CLOSED Which way does the graphed line point? The line points to the left the same way the arrow points. (…9,10,11)

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Example 3 Solve and graph 3 > h + 7 -7 -5 -7 -4 0 -4 > h -5 -5 ● -4 < h ●-5 1 1 -5 1 h > 20 20 21 22 Solution What inverse do we use first? We use the inverse of addition and subtract 7 from both sides. Do we have to flip the sign because of a negative inverse? YES or NO What inverse do we use next? We use the inverse of div. and mult. -5 on both sides. What is the proper way to write the solution? We write the solution with the variable in the front. What type of circle do we use on the # line? OPEN or CLOSED Which way does the graphed line point? The line points to the right the same way the arrow points. (21,22,23…)

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Example 4 Solve and Graph -3x + 3 > -36 -3 -3 0 -39 -3x > -39 -3x < -39 -3 x < 13 -13 0 13 Solution What inverse do we use first? We use the inverse of addition and subtract 3 from both sides. Do we have to flip the sign because of a negative inverse? YES or NO What inverse do we use next? We use the inverse of mult. and div. -3 on both sides. What type of circle do we use on the # line? OPEN or CLOSED Which way does the graphed line point? The line points to the left the same way the arrow points. (…11,12,13)

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