Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x+5)& = & 5 \color{red}{-} (2-5x) \\\Leftrightarrow & -6x+10& = &5-2+5x \\\Leftrightarrow & -6x \color{red}{+10} & = &3 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+10} \color{blue}{-10} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-10} \\\Leftrightarrow & -6x-5x& = &3-10 \\\Leftrightarrow & -11x& = &-7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x-4)& = & -4 \color{red}{-} (-15+x) \\\Leftrightarrow & 12x-24& = &-4+15-x \\\Leftrightarrow & 12x \color{red}{-24} & = &11 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &11 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 12x+x& = &11+24 \\\Leftrightarrow & 13x& = &35 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{35}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{35}{13} & & \\ & V = \left\{ \frac{35}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x-5)& = & -5 \color{red}{-} (-6-3x) \\\Leftrightarrow & 4x-10& = &-5+6+3x \\\Leftrightarrow & 4x \color{red}{-10} & = &1 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 4x-3x& = &1+10 \\\Leftrightarrow & x& = &11 \\ & V = \left\{ 11 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x+3)& = & -6 \color{red}{+} (15+x) \\\Leftrightarrow & -24x+12& = &-6+15+x \\\Leftrightarrow & -24x \color{red}{+12} & = &9 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &9-12 \\\Leftrightarrow & -25x& = &-3 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-3}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{3}{25} & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x+1)& = & 6 \color{red}{+} (13+x) \\\Leftrightarrow & 36x+6& = &6+13+x \\\Leftrightarrow & 36x \color{red}{+6} & = &19 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 36x-x& = &19-6 \\\Leftrightarrow & 35x& = &13 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{13}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{13}{35} & & \\ & V = \left\{ \frac{13}{35} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (4x+7)& = & -4 \color{red}{-} (-2+x) \\\Leftrightarrow & 20x+35& = &-4+2-x \\\Leftrightarrow & 20x \color{red}{+35} & = &-2 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 20x+x& = &-2-35 \\\Leftrightarrow & 21x& = &-37 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-37}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-37}{21} & & \\ & V = \left\{ \frac{-37}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (x-2)& = & 7 \color{red}{+} (5+3x) \\\Leftrightarrow & 2x-4& = &7+5+3x \\\Leftrightarrow & 2x \color{red}{-4} & = &12 \color{red}{+3x} \\\Leftrightarrow & 2x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 2x-3x& = &12+4 \\\Leftrightarrow & -x& = &16 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{16}{ \color{red}{-1} } \\\Leftrightarrow & x = -16 & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-6x+5)& = & -4 \color{red}{-} (-4+x) \\\Leftrightarrow & -30x+25& = &-4+4-x \\\Leftrightarrow & -30x \color{red}{+25} & = &0 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -30x+x& = &0-25 \\\Leftrightarrow & -29x& = &-25 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-25}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{25}{29} & & \\ & V = \left\{ \frac{25}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x+1)& = & 2 \color{red}{+} (14-3x) \\\Leftrightarrow & -4x+2& = &2+14-3x \\\Leftrightarrow & -4x \color{red}{+2} & = &16 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-2} \\\Leftrightarrow & -4x+3x& = &16-2 \\\Leftrightarrow & -x& = &14 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{14}{ \color{red}{-1} } \\\Leftrightarrow & x = -14 & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x-2)& = & -12 \color{red}{+} (13+x) \\\Leftrightarrow & 20x-10& = &-12+13+x \\\Leftrightarrow & 20x \color{red}{-10} & = &1 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 20x-x& = &1+10 \\\Leftrightarrow & 19x& = &11 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{11}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-x+2)& = & -4 \color{red}{+} (-4+3x) \\\Leftrightarrow & -2x+4& = &-4-4+3x \\\Leftrightarrow & -2x \color{red}{+4} & = &-8 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -2x-3x& = &-8-4 \\\Leftrightarrow & -5x& = &-12 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-12}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x-4)& = & -14 \color{red}{+} (1-2x) \\\Leftrightarrow & 15x-12& = &-14+1-2x \\\Leftrightarrow & 15x \color{red}{-12} & = &-13 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &-13 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & 15x+2x& = &-13+12 \\\Leftrightarrow & 17x& = &-1 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-1}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-1}{17} & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)