Math Help - solve and Graph the inequalities

1. solve and Graph the inequalities

1. 4x + y > 4

2. 3x - 4y < 12

3. You have at least $30 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer. 2. Originally Posted by Patience 1. 4x + y > 4 2. 3x - 4y < 12 3. You have at least$30 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer.
1. 4x + y > 4
4x + y >= 4
y >= -4x + 4

this is a straight line with slope -4 and y-intercept 4. we want all values above this line. see graph1 below

2. 3x - 4y < 12
3x - 4y < 12
-4y < -3x + 12
y > (3/4)x - 3 .........since i divided both sides by a negative number, i turn around the inequality sign

now this is a line with slope 3/4 and y-intercept -3. we want all values above that line. see graph2 below

3. You have at least $30 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer. at least means you have greater than or equal to. a dime is 10cents, or$0.10, a quarter is 25 cents or \$0.25

let x be the number of dimes in the drawer
let y be the number of quarters in the drawer, then

0.10x + 0.25y >= 30

3. Originally Posted by Patience
1. 4x + y > 4

2. 3x - 4y < 12
...
Hello, Patience,

to 1.:

4x + y ≥ 4 ==> y ≥ -4x + 4

y = -4x + 4 is a straight line. With your inequality you are looking for those points of the coordinate plane which are above this line. The graph of the inequality is a half plane where the border (= the straight line) is included to the half plane. (yellow + orange)

to 2.:

3x - 4y < 12 ==> y > 3/4*x - 3

You get a half plane too which is above the straight line but the border doesn't belong to the half plane! Therefore the straight line is dotted. (orange + brown)

EB