Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x+5)& = & 11 \color{red}{-} (8+3x) \\\Leftrightarrow & 20x+20& = &11-8-3x \\\Leftrightarrow & 20x \color{red}{+20} & = &3 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 20x+3x& = &3-20 \\\Leftrightarrow & 23x& = &-17 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-17}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-17}{23} & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-3x-3)& = & -15 \color{red}{+} (-2+x) \\\Leftrightarrow & -15x-15& = &-15-2+x \\\Leftrightarrow & -15x \color{red}{-15} & = &-17 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -15x-x& = &-17+15 \\\Leftrightarrow & -16x& = &-2 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-2}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{1}{8} & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x+4)& = & 1 \color{red}{+} (-2+x) \\\Leftrightarrow & -4x+8& = &1-2+x \\\Leftrightarrow & -4x \color{red}{+8} & = &-1 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -4x-x& = &-1-8 \\\Leftrightarrow & -5x& = &-9 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-9}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{9}{5} & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x-4)& = & -8 \color{red}{+} (7+x) \\\Leftrightarrow & -24x-16& = &-8+7+x \\\Leftrightarrow & -24x \color{red}{-16} & = &-1 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -24x-x& = &-1+16 \\\Leftrightarrow & -25x& = &15 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{15}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-3}{5} & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (2x+6)& = & 7 \color{red}{-} (13+x) \\\Leftrightarrow & 12x+36& = &7-13-x \\\Leftrightarrow & 12x \color{red}{+36} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 12x+x& = &-6-36 \\\Leftrightarrow & 13x& = &-42 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-42}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-42}{13} & & \\ & V = \left\{ \frac{-42}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (2x-4)& = & -13 \color{red}{-} (-1+x) \\\Leftrightarrow & 6x-12& = &-13+1-x \\\Leftrightarrow & 6x \color{red}{-12} & = &-12 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 6x+x& = &-12+12 \\\Leftrightarrow & 7x& = &0 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{0}{ \color{red}{7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-6x+4)& = & -11 \color{red}{+} (3+x) \\\Leftrightarrow & -12x+8& = &-11+3+x \\\Leftrightarrow & -12x \color{red}{+8} & = &-8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -12x-x& = &-8-8 \\\Leftrightarrow & -13x& = &-16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (2x-1)& = & -14 \color{red}{+} (-8+x) \\\Leftrightarrow & 12x-6& = &-14-8+x \\\Leftrightarrow & 12x \color{red}{-6} & = &-22 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 12x-x& = &-22+6 \\\Leftrightarrow & 11x& = &-16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x+6)& = & 11 \color{red}{-} (9+x) \\\Leftrightarrow & -12x+18& = &11-9-x \\\Leftrightarrow & -12x \color{red}{+18} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &2-18 \\\Leftrightarrow & -11x& = &-16 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-16}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-x+3)& = & 8 \color{red}{-} (12+x) \\\Leftrightarrow & -2x+6& = &8-12-x \\\Leftrightarrow & -2x \color{red}{+6} & = &-4 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -2x+x& = &-4-6 \\\Leftrightarrow & -x& = &-10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-10}{ \color{red}{-1} } \\\Leftrightarrow & x = 10 & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (2x+1)& = & -9 \color{red}{-} (-11-5x) \\\Leftrightarrow & 8x+4& = &-9+11+5x \\\Leftrightarrow & 8x \color{red}{+4} & = &2 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & 8x-5x& = &2-4 \\\Leftrightarrow & 3x& = &-2 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-2}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x-6)& = & 3 \color{red}{-} (-3+x) \\\Leftrightarrow & -10x-30& = &3+3-x \\\Leftrightarrow & -10x \color{red}{-30} & = &6 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -10x+x& = &6+30 \\\Leftrightarrow & -9x& = &36 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{36}{ \color{red}{-9} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)