Question

geometry/transitional math
multi - step equations
solve each equation.

1. $x - 4 - 1=-9$
2. $k + 2+3 = 3$
3. $-r + 4r=-12$
4. $2n-5n = 6$
5. $-3 = 2x-5-3x$
6. $0 = 4a + 6a$
7. $-6n-5n = 11$
8. $-a + 5a=-8$
9. $1=x + 1+x$
10. $-10 = 6m-5-m$
11. $4v-4-v=-7$
12. $-5r-r=-18$
13. $2 = 4r-2r$
14. $a-5 + 3a = 15$
15. $5b + 4+6 = 10$
16. $-16=-5x-3x$
17. $p-5-2=-9$
18. $-b + 6b = 15$
19. $3r + 5r = 16$
20. $15=n-1 + 3n$

Explanation:

Step1: Simplify left - hand side

For equation (1) $x - 4-1=-9$, simplify the left - hand side to get $x-(4 + 1)=x - 5$. So the equation becomes $x-5=-9$.

Step2: Isolate the variable

Add 5 to both sides of $x - 5=-9$. We have $x=-9 + 5=-4$.

For equation (2) $k+2 + 3=3$, simplify the left - hand side: $k+(2 + 3)=k + 5$. So $k+5=3$. Subtract 5 from both sides, $k=3-5=-2$.

For equation (3) $-r + 4r=-12$, combine like terms on the left - hand side: $(-1 + 4)r=3r$. So $3r=-12$. Divide both sides by 3, $r=\frac{-12}{3}=-4$.

For equation (4) $2n-5n=6$, combine like terms: $(2 - 5)n=-3n$. So $-3n=6$. Divide both sides by - 3, $n=\frac{6}{-3}=-2$.

For equation (5) $-3=2x-5-3x$, combine like terms on the right - hand side: $2x-3x-5=-x - 5$. So $-x-5=-3$. Add 5 to both sides: $-x=-3 + 5 = 2$. Multiply both sides by - 1, $x=-2$.

For equation (6) $0=4a+6a$, combine like terms: $(4 + 6)a=10a$. So $10a=0$. Divide both sides by 10, $a = 0$.

For equation (7) $-6n-5n=11$, combine like terms: $(-6-5)n=-11n$. So $-11n=11$. Divide both sides by - 11, $n=-1$.

For equation (8) $-a + 5a=-8$, combine like terms: $(-1 + 5)a=4a$. So $4a=-8$. Divide both sides by 4, $a=-2$.

For equation (9) $1=x + 1+x$, combine like terms: $1=(1 + 1)x+1=2x+1$. Subtract 1 from both sides: $2x=1 - 1=0$. Divide both sides by 2, $x = 0$.

For equation (10) $-10=6m-5-m$, combine like terms: $-10=(6 - 1)m-5=5m-5$. Add 5 to both sides: $5m=-10 + 5=-5$. Divide both sides by 5, $m=-1$.

For equation (11) $4v-4-v=-7$, combine like terms: $(4 - 1)v-4=3v-4$. So $3v-4=-7$. Add 4 to both sides: $3v=-7 + 4=-3$. Divide both sides by 3, $v=-1$.

For equation (12) $-5r-r=-18$, combine like terms: $(-5-1)r=-6r$. So $-6r=-18$. Divide both sides by - 6, $r = 3$.

For equation (13) $2=4r-2r$, combine like terms: $2=(4 - 2)r=2r$. Divide both sides by 2, $r = 1$.

For equation (14) $a-5+3a=15$, combine like terms: $(1 + 3)a-5=4a-5$. So $4a-5=15$. Add 5 to both sides: $4a=15 + 5=20$. Divide both sides by 4, $a = 5$.

For equation (15) $5b+4 + 6=10$, simplify the left - hand side: $5b+(4 + 6)=5b+10$. So $5b+10=10$. Subtract 10 from both sides: $5b=10 - 10=0$. Divide both sides by 5, $b = 0$.

For equation (16) $-16=-5x-3x$, combine like terms: $-16=(-5-3)x=-8x$. Divide both sides by - 8, $x = 2$.

For equation (17) $p-5-2=-9$, simplify the left - hand side: $p-(5 + 2)=p - 7$. So $p-7=-9$. Add 7 to both sides: $p=-9+7=-2$.

For equation (18) $-b + 6b=15$, combine like terms: $(-1 + 6)b=5b$. So $5b=15$. Divide both sides by 5, $b = 3$.

For equation (19) $3r+5r=16$, combine like terms: $(3 + 5)r=8r$. So $8r=16$. Divide both sides by 8, $r = 2$.

For equation (20) $15=n-1+3n$, combine like terms: $15=(1 + 3)n-1=4n-1$. Add 1 to both sides: $4n=15 + 1=16$. Divide both sides by 4, $n = 4$.

Answer:

1. $x=-4$
2. $k=-2$
3. $r=-4$
4. $n=-2$
5. $x=-2$
6. $a = 0$
7. $n=-1$
8. $a=-2$
9. $x = 0$
10. $m=-1$
11. $v=-1$
12. $r = 3$
13. $r = 1$
14. $a = 5$
15. $b = 0$
16. $x = 2$
17. $p=-2$
18. $b = 3$
19. $r = 2$
20. $n = 4$