Answer:
All real numbers are solutions.
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
4(3x+2)=16x+7−4x+1
(4)(3x)+(4)(2)=16x+7+−4x+1(Distribute)
12x+8=16x+7+−4x+1
12x+8=(16x+−4x)+(7+1)(Combine Like Terms)
12x+8=12x+8
12x+8=12x+8
Step 2: Subtract 12x from both sides.
12x+8−12x=12x+8−12x
8=8
Step 3: Subtract 8 from both sides.
8−8=8−8
0=0
Answer:
Find the ratio of hops to distance traveled (1: 1.5), then multiply 150 by 1.5.
Step-by-step explanation:
A child is hopping along a sidewalk. The ratio table below shows the comparison between the number of hops and the distance traveled. Hopping Number of hops Distance traveled (ft) 20 30 50 75 80 120 150 ?
Which statement correctly explains how to find the distance traveled after 150 hops? Subtract 120 – 75 to get 45, then add that number to 120. Add 30 + 75 + 120. Find the ratio of hops to distance traveled (1:1.5), then multiply 150 by 1.5. Find the ratio of hops to distance traveled (1:1.5), then divide 150 by 1.5.
Solution:
The table is:
No. of hops Distance traveled
20 30
50 75
80 120
150 ?
From the table, for every 30 increase in the number of hops, the distance travelled increase by 45 feet
Find the slope of the line:
m = (y2-y1) / (x2-x1)
m=slope of the line
y2-y1 = change in distance travelled
x-2 - x1 = Change in number of hops
m = (y2-y1) / (x2-x1)
m = (75-30) / (50-20)
=45 / 30
m = 1.5
Then, the line is:
y = 1.5x
We substitute x = 150
y = 1.5x
y = 1.5 × 150
y = 225
