Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x+3)& = & -11 \color{red}{-} (-11-5x) \\\Leftrightarrow & -6x+6& = &-11+11+5x \\\Leftrightarrow & -6x \color{red}{+6} & = &0 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & -6x-5x& = &0-6 \\\Leftrightarrow & -11x& = &-6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x+6)& = & 3 \color{red}{-} (-12+3x) \\\Leftrightarrow & 2x+12& = &3+12-3x \\\Leftrightarrow & 2x \color{red}{+12} & = &15 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &15 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & 2x+3x& = &15-12 \\\Leftrightarrow & 5x& = &3 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{3}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x-7)& = & 12 \color{red}{-} (6-5x) \\\Leftrightarrow & -8x-28& = &12-6+5x \\\Leftrightarrow & -8x \color{red}{-28} & = &6 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{-5x} & = &6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+28} \\\Leftrightarrow & -8x-5x& = &6+28 \\\Leftrightarrow & -13x& = &34 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{34}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-34}{13} & & \\ & V = \left\{ \frac{-34}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x-6)& = & -13 \color{red}{+} (-1+x) \\\Leftrightarrow & 18x-36& = &-13-1+x \\\Leftrightarrow & 18x \color{red}{-36} & = &-14 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 18x-x& = &-14+36 \\\Leftrightarrow & 17x& = &22 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{22}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{22}{17} & & \\ & V = \left\{ \frac{22}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-6x-2)& = & -1 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x-4& = &-1+13-x \\\Leftrightarrow & -12x \color{red}{-4} & = &12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -12x+x& = &12+4 \\\Leftrightarrow & -11x& = &16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x-3)& = & -3 \color{red}{+} (-9+x) \\\Leftrightarrow & 24x-18& = &-3-9+x \\\Leftrightarrow & 24x \color{red}{-18} & = &-12 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 24x-x& = &-12+18 \\\Leftrightarrow & 23x& = &6 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{6}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-x-2)& = & -7 \color{red}{+} (-14+x) \\\Leftrightarrow & -4x-8& = &-7-14+x \\\Leftrightarrow & -4x \color{red}{-8} & = &-21 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -4x-x& = &-21+8 \\\Leftrightarrow & -5x& = &-13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-1)& = & 8 \color{red}{+} (-13-2x) \\\Leftrightarrow & -15x-3& = &8-13-2x \\\Leftrightarrow & -15x \color{red}{-3} & = &-5 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &-5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & -15x+2x& = &-5+3 \\\Leftrightarrow & -13x& = &-2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-6x-5)& = & -5 \color{red}{+} (-14+x) \\\Leftrightarrow & -30x-25& = &-5-14+x \\\Leftrightarrow & -30x \color{red}{-25} & = &-19 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & -30x-x& = &-19+25 \\\Leftrightarrow & -31x& = &6 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{6}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-6}{31} & & \\ & V = \left\{ \frac{-6}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x+5)& = & 13 \color{red}{+} (4-3x) \\\Leftrightarrow & -4x+20& = &13+4-3x \\\Leftrightarrow & -4x \color{red}{+20} & = &17 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -4x+3x& = &17-20 \\\Leftrightarrow & -x& = &-3 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-3}{ \color{red}{-1} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x-5)& = & 9 \color{red}{+} (-13+x) \\\Leftrightarrow & 20x-25& = &9-13+x \\\Leftrightarrow & 20x \color{red}{-25} & = &-4 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+25} \\\Leftrightarrow & 20x-x& = &-4+25 \\\Leftrightarrow & 19x& = &21 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{21}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{21}{19} & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (x+6)& = & 11 \color{red}{+} (8+4x) \\\Leftrightarrow & 3x+18& = &11+8+4x \\\Leftrightarrow & 3x \color{red}{+18} & = &19 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{-4x} & = &19 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-18} \\\Leftrightarrow & 3x-4x& = &19-18 \\\Leftrightarrow & -x& = &1 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{1}{ \color{red}{-1} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)