Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-4x-3)& = & 13 \color{red}{+} (2-3x) \\\Leftrightarrow & -16x-12& = &13+2-3x \\\Leftrightarrow & -16x \color{red}{-12} & = &15 \color{red}{-3x} \\\Leftrightarrow & -16x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &15 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & -16x+3x& = &15+12 \\\Leftrightarrow & -13x& = &27 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{27}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-27}{13} & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-4x+6)& = & -5 \color{red}{+} (15+x) \\\Leftrightarrow & -12x+18& = &-5+15+x \\\Leftrightarrow & -12x \color{red}{+18} & = &10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -12x-x& = &10-18 \\\Leftrightarrow & -13x& = &-8 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-8}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-3x-1)& = & -13 \color{red}{-} (-2-5x) \\\Leftrightarrow & -18x-6& = &-13+2+5x \\\Leftrightarrow & -18x \color{red}{-6} & = &-11 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -18x-5x& = &-11+6 \\\Leftrightarrow & -23x& = &-5 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-5}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{5}{23} & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-5x-4)& = & -14 \color{red}{+} (8+x) \\\Leftrightarrow & -15x-12& = &-14+8+x \\\Leftrightarrow & -15x \color{red}{-12} & = &-6 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -15x-x& = &-6+12 \\\Leftrightarrow & -16x& = &6 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{6}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-3}{8} & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x-6)& = & -14 \color{red}{+} (13+3x) \\\Leftrightarrow & -4x-24& = &-14+13+3x \\\Leftrightarrow & -4x \color{red}{-24} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-24} \color{blue}{+24} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+24} \\\Leftrightarrow & -4x-3x& = &-1+24 \\\Leftrightarrow & -7x& = &23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-23}{7} & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x-4)& = & -13 \color{red}{+} (8+x) \\\Leftrightarrow & -12x-8& = &-13+8+x \\\Leftrightarrow & -12x \color{red}{-8} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -12x-x& = &-5+8 \\\Leftrightarrow & -13x& = &3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-5)& = & 9 \color{red}{+} (-12+x) \\\Leftrightarrow & 8x-20& = &9-12+x \\\Leftrightarrow & 8x \color{red}{-20} & = &-3 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 8x-x& = &-3+20 \\\Leftrightarrow & 7x& = &17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-4x-1)& = & -13 \color{red}{+} (5+x) \\\Leftrightarrow & -12x-3& = &-13+5+x \\\Leftrightarrow & -12x \color{red}{-3} & = &-8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -12x-x& = &-8+3 \\\Leftrightarrow & -13x& = &-5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (5x+6)& = & 3 \color{red}{+} (4+3x) \\\Leftrightarrow & 10x+12& = &3+4+3x \\\Leftrightarrow & 10x \color{red}{+12} & = &7 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 10x-3x& = &7-12 \\\Leftrightarrow & 7x& = &-5 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-5}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x+2)& = & 4 \color{red}{+} (-1+x) \\\Leftrightarrow & 4x+4& = &4-1+x \\\Leftrightarrow & 4x \color{red}{+4} & = &3 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 4x-x& = &3-4 \\\Leftrightarrow & 3x& = &-1 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-1}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x+6)& = & 11 \color{red}{-} (-10+x) \\\Leftrightarrow & 20x+30& = &11+10-x \\\Leftrightarrow & 20x \color{red}{+30} & = &21 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 20x+x& = &21-30 \\\Leftrightarrow & 21x& = &-9 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-9}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-3x+6)& = & -5 \color{red}{+} (-9+x) \\\Leftrightarrow & -6x+12& = &-5-9+x \\\Leftrightarrow & -6x \color{red}{+12} & = &-14 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -6x-x& = &-14-12 \\\Leftrightarrow & -7x& = &-26 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-26}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{26}{7} & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)