Zahra wants the equation below to have an infinite number of solutions when the missing number is placed in the box.

Box (x minus 3) + 2 x = negative (x minus 5) + 4

c = -3

Step-by-step explanation:

Call the unknown c

c(x-3) +2x = -(x-5) +4

Distribute the negative sign

c(x-3) +2x = -x+5+4

Combine like terms

c(x-3) +2x = -x +9

Subtract 2x from each side

c(x-3) +2x-2x = -x-2x +9

c(x-3) = -3x+9

Factor a -3 from the right side

c(x-3) = -3(x-3)

Divide by (x-3)

c = -3

The right and left hand side need to be equal for there to be infinite solutions, so c = -3

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."