Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x+4)& = & -14 \color{red}{-} (9+x) \\\Leftrightarrow & -6x+8& = &-14-9-x \\\Leftrightarrow & -6x \color{red}{+8} & = &-23 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -6x+x& = &-23-8 \\\Leftrightarrow & -5x& = &-31 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-31}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{31}{5} & & \\ & V = \left\{ \frac{31}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x-1)& = & 8 \color{red}{+} (-14+x) \\\Leftrightarrow & -24x-4& = &8-14+x \\\Leftrightarrow & -24x \color{red}{-4} & = &-6 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -24x-x& = &-6+4 \\\Leftrightarrow & -25x& = &-2 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-2}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{2}{25} & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (6x+3)& = & 2 \color{red}{-} (2+x) \\\Leftrightarrow & 12x+6& = &2-2-x \\\Leftrightarrow & 12x \color{red}{+6} & = &0 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &0-6 \\\Leftrightarrow & 13x& = &-6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x+6)& = & 10 \color{red}{-} (5-2x) \\\Leftrightarrow & -15x+30& = &10-5+2x \\\Leftrightarrow & -15x \color{red}{+30} & = &5 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+30} \color{blue}{-30} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-30} \\\Leftrightarrow & -15x-2x& = &5-30 \\\Leftrightarrow & -17x& = &-25 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-25}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{25}{17} & & \\ & V = \left\{ \frac{25}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-x-4)& = & -12 \color{red}{+} (-12+3x) \\\Leftrightarrow & -5x-20& = &-12-12+3x \\\Leftrightarrow & -5x \color{red}{-20} & = &-24 \color{red}{+3x} \\\Leftrightarrow & -5x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-24 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -5x-3x& = &-24+20 \\\Leftrightarrow & -8x& = &-4 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-4}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{1}{2} & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x-6)& = & -6 \color{red}{-} (4-3x) \\\Leftrightarrow & 4x-12& = &-6-4+3x \\\Leftrightarrow & 4x \color{red}{-12} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 4x-3x& = &-10+12 \\\Leftrightarrow & x& = &2 \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-x-5)& = & -7 \color{red}{-} (-2+x) \\\Leftrightarrow & -2x-10& = &-7+2-x \\\Leftrightarrow & -2x \color{red}{-10} & = &-5 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -2x+x& = &-5+10 \\\Leftrightarrow & -x& = &5 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{5}{ \color{red}{-1} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x-3)& = & 9 \color{red}{-} (-2+x) \\\Leftrightarrow & 30x-18& = &9+2-x \\\Leftrightarrow & 30x \color{red}{-18} & = &11 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 30x+x& = &11+18 \\\Leftrightarrow & 31x& = &29 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{29}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{29}{31} & & \\ & V = \left\{ \frac{29}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x+3)& = & 2 \color{red}{+} (2-2x) \\\Leftrightarrow & 15x+15& = &2+2-2x \\\Leftrightarrow & 15x \color{red}{+15} & = &4 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{+2x} & = &4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-15} \\\Leftrightarrow & 15x+2x& = &4-15 \\\Leftrightarrow & 17x& = &-11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-11}{17} & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x+7)& = & 10 \color{red}{-} (-6+x) \\\Leftrightarrow & 12x+21& = &10+6-x \\\Leftrightarrow & 12x \color{red}{+21} & = &16 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 12x+x& = &16-21 \\\Leftrightarrow & 13x& = &-5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (6x-7)& = & 14 \color{red}{-} (8+x) \\\Leftrightarrow & 12x-14& = &14-8-x \\\Leftrightarrow & 12x \color{red}{-14} & = &6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 12x+x& = &6+14 \\\Leftrightarrow & 13x& = &20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{20}{13} & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-5x-3)& = & 2 \color{red}{-} (-2+4x) \\\Leftrightarrow & -15x-9& = &2+2-4x \\\Leftrightarrow & -15x \color{red}{-9} & = &4 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-9} \color{blue}{+9} \color{blue}{+4x} & = &4 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+9} \\\Leftrightarrow & -15x+4x& = &4+9 \\\Leftrightarrow & -11x& = &13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)