Theres an app called photomath that could easily solve problems like this
<span>4|2x − 2| + 10 = 34
</span><span>4|2x − 2| + 10 - 10 = 34 - 10
</span><span>4|2x − 2| = 24
</span><span>|2x − 2| = 24/4 = 6
2x - 2 = 6 or 2x - 2 = -6
2x = 6 + 2 or 2x = -6 + 2
2x = 8 or 2x = -4
x = 8/2 or x = -4/2
x = 4 or x = -2
To check for extraneous solutions:
</span>For x = 4: <span>
4|2(4) − 2| + 10 = 34
4</span><span>|8 − 2| = 34 - 10 = 24
6 = 24/4 = 6 (solution is valid)
</span><span>For x = -2: <span>
4|2(-2) − 2| + 10 = 34
4</span><span>|-4 − 2| = 34 - 10 = 24
</span></span><span><span><span>|-6| = </span>6 = 24/4 = 6 (solution is valid) </span>
</span>
Therefore, solutions are x = 4 , x = -2
It is A because the ratio is 2:3
Answer:
The inequality in this case is 100 + 400*t > 500 + 350*t and for B to be cheaper Sophia has to rent it for more than 8 months.
Step-by-step explanation:
In order to write the inequality we first need to write two equations one for each apartment. For apartment A we have a fixed cost of $100 and a variable cost of $400 that varies according to the time living in there, so we have:
rent = 100 + 400*t
For apartment B we have a fixed cost of $500 and a variable cost of $350 that varies according to the time living in there, so we have:
rent = 500 + 350*t
In order for the total paid in B to be less than for the one in A we need to satisfy the following inequality:
100 + 400*t > 500 + 350*t
400*t - 350*t > 500 - 100
50*t > 400
t > 400/50
t > 8 months
The inequality in this case is 100 + 400*t > 500 + 350*t and for B to be cheaper Sophia has to rent it for more than 8 months.
