Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-x-5)& = & 7 \color{red}{+} (-11+x) \\\Leftrightarrow & -2x-10& = &7-11+x \\\Leftrightarrow & -2x \color{red}{-10} & = &-4 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & -2x-x& = &-4+10 \\\Leftrightarrow & -3x& = &6 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{6}{ \color{red}{-3} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (6x+5)& = & 15 \color{red}{+} (-6+x) \\\Leftrightarrow & 24x+20& = &15-6+x \\\Leftrightarrow & 24x \color{red}{+20} & = &9 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 24x-x& = &9-20 \\\Leftrightarrow & 23x& = &-11 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-11}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-11}{23} & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-3x-6)& = & 4 \color{red}{-} (-5-2x) \\\Leftrightarrow & -15x-30& = &4+5+2x \\\Leftrightarrow & -15x \color{red}{-30} & = &9 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-30} \color{blue}{+30} \color{blue}{-2x} & = &9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+30} \\\Leftrightarrow & -15x-2x& = &9+30 \\\Leftrightarrow & -17x& = &39 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{39}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-39}{17} & & \\ & V = \left\{ \frac{-39}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (4x+1)& = & -4 \color{red}{-} (12+x) \\\Leftrightarrow & 12x+3& = &-4-12-x \\\Leftrightarrow & 12x \color{red}{+3} & = &-16 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 12x+x& = &-16-3 \\\Leftrightarrow & 13x& = &-19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x+6)& = & 8 \color{red}{-} (5+3x) \\\Leftrightarrow & -8x+12& = &8-5-3x \\\Leftrightarrow & -8x \color{red}{+12} & = &3 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -8x+3x& = &3-12 \\\Leftrightarrow & -5x& = &-9 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-9}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{9}{5} & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-x+5)& = & 14 \color{red}{+} (5-5x) \\\Leftrightarrow & -3x+15& = &14+5-5x \\\Leftrightarrow & -3x \color{red}{+15} & = &19 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{+15} \color{blue}{-15} \color{blue}{+5x} & = &19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-15} \\\Leftrightarrow & -3x+5x& = &19-15 \\\Leftrightarrow & 2x& = &4 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{4}{ \color{red}{2} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x-3)& = & -1 \color{red}{-} (11+x) \\\Leftrightarrow & -30x-15& = &-1-11-x \\\Leftrightarrow & -30x \color{red}{-15} & = &-12 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -30x+x& = &-12+15 \\\Leftrightarrow & -29x& = &3 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{3}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-3}{29} & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x-3)& = & -12 \color{red}{-} (-4+x) \\\Leftrightarrow & -3x-9& = &-12+4-x \\\Leftrightarrow & -3x \color{red}{-9} & = &-8 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -3x+x& = &-8+9 \\\Leftrightarrow & -2x& = &1 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{1}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x+7)& = & -13 \color{red}{+} (8+x) \\\Leftrightarrow & -2x+14& = &-13+8+x \\\Leftrightarrow & -2x \color{red}{+14} & = &-5 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -2x-x& = &-5-14 \\\Leftrightarrow & -3x& = &-19 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-19}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{19}{3} & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x+5)& = & -3 \color{red}{-} (-3+x) \\\Leftrightarrow & 24x+30& = &-3+3-x \\\Leftrightarrow & 24x \color{red}{+30} & = &0 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 24x+x& = &0-30 \\\Leftrightarrow & 25x& = &-30 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-30}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (3x+2)& = & -14 \color{red}{+} (4+x) \\\Leftrightarrow & 12x+8& = &-14+4+x \\\Leftrightarrow & 12x \color{red}{+8} & = &-10 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 12x-x& = &-10-8 \\\Leftrightarrow & 11x& = &-18 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-18}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-18}{11} & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x+3)& = & 3 \color{red}{-} (-3-2x) \\\Leftrightarrow & 15x+9& = &3+3+2x \\\Leftrightarrow & 15x \color{red}{+9} & = &6 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+9} \color{blue}{-9} \color{blue}{-2x} & = &6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-9} \\\Leftrightarrow & 15x-2x& = &6-9 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)