−7x+1≥22
-7x ≥ 21
x ≤ -3
-10x+41 ≥ 81
-10x ≥ 40
x ≤ -4
so, what do you think?
-7x ≥ 21
x ≤ -3
-10x+41 ≥ 81
-10x ≥ 40
x ≤ -4
so, what do you think?
Let's start with the first inequality: −7x + 1 ≥ 22.
Step 1: Subtract 1 from both sides of the inequality:
−7x + 1 - 1 ≥ 22 - 1
Simplifying, we get:
−7x ≥ 21
Step 2: Divide both sides of the inequality by -7. Remember that when dividing by a negative number, the inequality sign flips:
−7x/−7 ≤ 21/−7
Simplifying further, we have:
x ≤ -3
Now let's move on to the second inequality: −10x + 41 ≥ 81.
Step 1: Subtract 41 from both sides of the inequality:
−10x + 41 - 41 ≥ 81 - 41
Simplifying:
−10x ≥ 40
Step 2: Divide both sides of the inequality by -10:
−10x/−10 ≤ 40/−10
Simplifying further:
x ≤ -4
So, the solutions for x that satisfy either one of the inequalities are x ≤ -3 or x ≤ -4.
Solving the first inequality, −7x + 1 ≥ 22:
1. Subtract 1 from both sides to get −7x ≥ 21.
−7x ≥ 21
2. Divide both sides by −7. Remember when dividing by a negative number, the inequality sign flips.
x ≤ 21/-7
x ≤ -3
So, the solution to the first inequality is x ≤ -3.
Solving the second inequality, −10x + 41 ≥ 81:
1. Subtract 41 from both sides to get −10x ≥ 40.
−10x ≥ 40
2. Divide both sides by −10. Remember when dividing by a negative number, the inequality sign flips.
x ≤ 40/-10
x ≤ -4
So, the solution to the second inequality is x ≤ -4.
Finally, to combine the solutions, we take the intersection of the two solution sets:
x ≤ -3 AND x ≤ -4
Since both inequalities have the same solution, we can rewrite it as:
x ≤ -4
Therefore, the solution to the given system of inequalities is x ≤ -4.