Question

algebra 1 semester 1 cornell notes standards: ps.2, ps.4, ai.l.1, and ai.l.2 learning target: students will be able to...:; - justify/explain the steps taken when solving inequalities - justify/explain the terms as to when an inequality symbol changes direction when solving and inequality. - identify the key words within a real-world scenario to represent an inequality. - form an inequality from a real-world scenario in one variable and solve it. - defend the validity of a solution to a real-world scenario success criteria: i can..... - adapt an inequality in one variable with variables on both sides, combining like terms, and the distributive property while following the correct steps when solving an inequality. - identify when solving an inequality the conditions as to which the inequality symbol needs to change directions to make the inequality statement true. - describe in words the steps taken when solving inequalities - develop an inequality using key words within a real-world scenario - justify whether or not a solution is reasonable given a real world scenario. essential question: what purpose(s) can inequalities be used for in the real world setting? questions/examples: the steps to solving and inequality are the same as solving an equation when multiplying or dividing by a negative to get a variable by itself you must change/flip your inequality sign. see below 5 - 2x < 15 -5 -5 (-2x)/(-2) < 10/(-2) x > -5 5.1 notes: 5-1 vocabulary: inequality: an open sentence that contains the following <, >, ≤ or ≥ conceptsummary phrases for inequalities <: less than, fewer than >: greater than, more than ≤: at most, no more than, less than or equal to ≥: at least, no less than, greater than or equal to ex. 1: solve c - 12 > 65. check your solution. ex. 2: solve k - 4 < 10. ex. 3: solve -2x + 8 ≤ -4x ex. 4: solve 12n - 4 ≤ 13n. graph the solution. -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 name: jess class/block: 1 date: 12-10-11 book: hw:

Explanation:

Step1: Solve \( c - 12 > 65 \)

To isolate \( c \), add 12 to both sides of the inequality.
\( c - 12 + 12 > 65 + 12 \)
Simplify both sides: \( c > 77 \).

Step2: Check the solution

Pick a value greater than 77, say \( c = 80 \). Substitute into the original inequality:
\( 80 - 12 = 68 \), and \( 68 > 65 \), which is true.

Answer:

The solution to \( c - 12 > 65 \) is \( c > 77 \).