Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-2)& = & -6 \color{red}{+} (1-5x) \\\Leftrightarrow & 3x-6& = &-6+1-5x \\\Leftrightarrow & 3x \color{red}{-6} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 3x+5x& = &-5+6 \\\Leftrightarrow & 8x& = &1 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{1}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{1}{8} & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x-3)& = & -13 \color{red}{-} (-9+x) \\\Leftrightarrow & 20x-12& = &-13+9-x \\\Leftrightarrow & 20x \color{red}{-12} & = &-4 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 20x+x& = &-4+12 \\\Leftrightarrow & 21x& = &8 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{8}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{8}{21} & & \\ & V = \left\{ \frac{8}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x+2)& = & -2 \color{red}{+} (-2-3x) \\\Leftrightarrow & -10x+4& = &-2-2-3x \\\Leftrightarrow & -10x \color{red}{+4} & = &-4 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & -10x+3x& = &-4-4 \\\Leftrightarrow & -7x& = &-8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (2x-4)& = & 7 \color{red}{-} (-10+x) \\\Leftrightarrow & 8x-16& = &7+10-x \\\Leftrightarrow & 8x \color{red}{-16} & = &17 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 8x+x& = &17+16 \\\Leftrightarrow & 9x& = &33 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{33}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{11}{3} & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x-3)& = & -1 \color{red}{+} (6+x) \\\Leftrightarrow & 24x-12& = &-1+6+x \\\Leftrightarrow & 24x \color{red}{-12} & = &5 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &5+12 \\\Leftrightarrow & 23x& = &17 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{17}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{17}{23} & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x-6)& = & -15 \color{red}{-} (-8-2x) \\\Leftrightarrow & 15x-30& = &-15+8+2x \\\Leftrightarrow & 15x \color{red}{-30} & = &-7 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-30} \color{blue}{+30} \color{blue}{-2x} & = &-7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+30} \\\Leftrightarrow & 15x-2x& = &-7+30 \\\Leftrightarrow & 13x& = &23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (x-4)& = & 3 \color{red}{+} (-4-5x) \\\Leftrightarrow & 6x-24& = &3-4-5x \\\Leftrightarrow & 6x \color{red}{-24} & = &-1 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 6x+5x& = &-1+24 \\\Leftrightarrow & 11x& = &23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x+3)& = & 12 \color{red}{+} (3+2x) \\\Leftrightarrow & -9x+9& = &12+3+2x \\\Leftrightarrow & -9x \color{red}{+9} & = &15 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{-2x} & = &15 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-9} \\\Leftrightarrow & -9x-2x& = &15-9 \\\Leftrightarrow & -11x& = &6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-4x-3)& = & -15 \color{red}{+} (11+x) \\\Leftrightarrow & -12x-9& = &-15+11+x \\\Leftrightarrow & -12x \color{red}{-9} & = &-4 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -12x-x& = &-4+9 \\\Leftrightarrow & -13x& = &5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-5}{13} & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x-3)& = & 10 \color{red}{+} (7+3x) \\\Leftrightarrow & -10x-6& = &10+7+3x \\\Leftrightarrow & -10x \color{red}{-6} & = &17 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &17 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & -10x-3x& = &17+6 \\\Leftrightarrow & -13x& = &23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x+1)& = & 1 \color{red}{+} (-9+x) \\\Leftrightarrow & -20x+4& = &1-9+x \\\Leftrightarrow & -20x \color{red}{+4} & = &-8 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -20x-x& = &-8-4 \\\Leftrightarrow & -21x& = &-12 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-12}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x+7)& = & 1 \color{red}{+} (-8+x) \\\Leftrightarrow & -24x+28& = &1-8+x \\\Leftrightarrow & -24x \color{red}{+28} & = &-7 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -24x-x& = &-7-28 \\\Leftrightarrow & -25x& = &-35 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-35}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)