1). A sales representative is given a choice of tow paychecks plans. One choice includes a monthly base pay of $300 plus 10% od his sales. The second choice is a monthly salary of $1200. For what amount of sales would the representative make more money with the first plan?
2). 4 > x - 3(x + 2)
3). -2 > 7x - 2(x - 4)
Can anyone assist me?
I do not understand this.
23
2) 4>x-3(x+2)
4>x-3x-6
4>-2x-6
10>-2x
-5<x
x>-5
300 + 0.1x >= 1200
0.1x >= 900
x >= 9000
1) To determine the amount of sales at which the sales representative would make more money with the first plan, we need to set up an equation where the earnings from the first plan are equal to the earnings from the second plan.
Let's assume the representative makes x dollars in sales.
For the first plan, the earnings would be the monthly base pay of $300 plus 10% of the sales. This can be expressed as 300 + 0.1x.
For the second plan, the earnings would be a monthly salary of $1200.
To find the point at which the earnings are equal, we set up the equation:
300 + 0.1x = 1200
Now we can solve for x:
0.1x = 1200 - 300
0.1x = 900
x = 900 / 0.1
x = 9000
Therefore, the sales representative would make more money with the first plan for sales amounts exceeding $9000.
2) To solve the inequality 4 > x - 3(x + 2), we need to simplify the expression and isolate x.
Start by distributing the -3 to both terms inside the parentheses:
4 > x - 3x - 6
Combine like terms:
4 > -2x - 6
Next, we can isolate the variable x by getting rid of the constant term on the right side:
Add 6 to both sides:
4 + 6 > -2x
Simplify:
10 > -2x
To isolate x, divide both sides by -2, remembering to flip the inequality sign when dividing by a negative number:
10 / -2 < x
Simplify:
-5 < x
Therefore, the solution to the inequality is x > -5.
3) To solve the inequality -2 > 7x - 2(x - 4), we need to simplify the expression and isolate x.
Start by distributing the -2 to both terms inside the parentheses:
-2 > 7x - 2x + 8
Combine like terms:
-2 > 5x + 8
Next, we can isolate the variable x by getting rid of the constant term on the right side:
Subtract 8 from both sides:
-2 - 8 > 5x
Simplify:
-10 > 5x
To isolate x, divide both sides by 5:
-10 / 5 > x
Simplify:
-2 > x
Therefore, the solution to the inequality is x < -2.