Elizabeth won a $300 gift certificate at silver gym. A membership costs $15 a month and has a one- time fee of $50. Complete the equation that models the number of months, x, her gift certificate is will pay for a Silver gym.

The correct answer is 15 x + 50 = 300

Explanation:

In an equation, the different values show a specific mathematical relationship, and the equality represented by the symbol (=) is used to find an unknown value. In the case presented, the unknown value is the number of months Elizabeth can pay using her $300 gift certificate. This means the letter x in the equation represents the number of months.

Moreover, this x should be multiplied by the month membership or $15 considering Elizabeth will need to pay this fee each month and this should be added to the one-time fee of $50. This implies the first part of the equation is 15x + 50. Finally, this value should be equal to the total money in the certificate or 300. According to this, the equation is 15x + 50 = 300.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be