Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

1. \(3(-x+3)=-15+(-2-2x)\)
2. \(6(2x+6)=-2-(-9+x)\)
3. \(3(3x+7)=-8+(10+x)\)
4. \(3(x+5)=-11+(-10-5x)\)
5. \(3(-3x-3)=-4-(-8-2x)\)
6. \(5(6x-6)=-4+(7+x)\)
7. \(5(-x-7)=4-(-2-4x)\)
8. \(4(-x-1)=14-(12+x)\)
9. \(2(-x+4)=-10-(-12+x)\)
10. \(2(5x+5)=10+(-14+x)\)
11. \(3(6x+2)=-3-(1+x)\)
12. \(2(3x+5)=-13-(7+x)\)

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-x+3)& = & -15 \color{red}{+} (-2-2x) \\\Leftrightarrow & -3x+9& = &-15-2-2x \\\Leftrightarrow & -3x \color{red}{+9} & = &-17 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{+9} \color{blue}{-9} \color{blue}{+2x} & = &-17 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-9} \\\Leftrightarrow & -3x+2x& = &-17-9 \\\Leftrightarrow & -x& = &-26 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-26}{ \color{red}{-1} } \\\Leftrightarrow & x = 26 & & \\ & V = \left\{ 26 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x+6)& = & -2 \color{red}{-} (-9+x) \\\Leftrightarrow & 12x+36& = &-2+9-x \\\Leftrightarrow & 12x \color{red}{+36} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 12x+x& = &7-36 \\\Leftrightarrow & 13x& = &-29 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-29}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (3x+7)& = & -8 \color{red}{+} (10+x) \\\Leftrightarrow & 9x+21& = &-8+10+x \\\Leftrightarrow & 9x \color{red}{+21} & = &2 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 9x-x& = &2-21 \\\Leftrightarrow & 8x& = &-19 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-19}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-19}{8} & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (x+5)& = & -11 \color{red}{+} (-10-5x) \\\Leftrightarrow & 3x+15& = &-11-10-5x \\\Leftrightarrow & 3x \color{red}{+15} & = &-21 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{+15} \color{blue}{-15} \color{blue}{+5x} & = &-21 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-15} \\\Leftrightarrow & 3x+5x& = &-21-15 \\\Leftrightarrow & 8x& = &-36 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-36}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-9}{2} & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-3x-3)& = & -4 \color{red}{-} (-8-2x) \\\Leftrightarrow & -9x-9& = &-4+8+2x \\\Leftrightarrow & -9x \color{red}{-9} & = &4 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & -9x-2x& = &4+9 \\\Leftrightarrow & -11x& = &13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x-6)& = & -4 \color{red}{+} (7+x) \\\Leftrightarrow & 30x-30& = &-4+7+x \\\Leftrightarrow & 30x \color{red}{-30} & = &3 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &3+30 \\\Leftrightarrow & 29x& = &33 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{33}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{33}{29} & & \\ & V = \left\{ \frac{33}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x-7)& = & 4 \color{red}{-} (-2-4x) \\\Leftrightarrow & -5x-35& = &4+2+4x \\\Leftrightarrow & -5x \color{red}{-35} & = &6 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-35} \color{blue}{+35} \color{blue}{-4x} & = &6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+35} \\\Leftrightarrow & -5x-4x& = &6+35 \\\Leftrightarrow & -9x& = &41 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{41}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-41}{9} & & \\ & V = \left\{ \frac{-41}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-x-1)& = & 14 \color{red}{-} (12+x) \\\Leftrightarrow & -4x-4& = &14-12-x \\\Leftrightarrow & -4x \color{red}{-4} & = &2 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -4x+x& = &2+4 \\\Leftrightarrow & -3x& = &6 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{6}{ \color{red}{-3} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x+4)& = & -10 \color{red}{-} (-12+x) \\\Leftrightarrow & -2x+8& = &-10+12-x \\\Leftrightarrow & -2x \color{red}{+8} & = &2 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -2x+x& = &2-8 \\\Leftrightarrow & -x& = &-6 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-6}{ \color{red}{-1} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (5x+5)& = & 10 \color{red}{+} (-14+x) \\\Leftrightarrow & 10x+10& = &10-14+x \\\Leftrightarrow & 10x \color{red}{+10} & = &-4 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 10x-x& = &-4-10 \\\Leftrightarrow & 9x& = &-14 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-14}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-14}{9} & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x+2)& = & -3 \color{red}{-} (1+x) \\\Leftrightarrow & 18x+6& = &-3-1-x \\\Leftrightarrow & 18x \color{red}{+6} & = &-4 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 18x+x& = &-4-6 \\\Leftrightarrow & 19x& = &-10 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-10}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-10}{19} & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x+5)& = & -13 \color{red}{-} (7+x) \\\Leftrightarrow & 6x+10& = &-13-7-x \\\Leftrightarrow & 6x \color{red}{+10} & = &-20 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 6x+x& = &-20-10 \\\Leftrightarrow & 7x& = &-30 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-30}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-30}{7} & & \\ & V = \left\{ \frac{-30}{7} \right\} & \\\end{align}\)