Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x+5)& = & 8 \color{red}{+} (8-3x) \\\Leftrightarrow & 16x+20& = &8+8-3x \\\Leftrightarrow & 16x \color{red}{+20} & = &16 \color{red}{-3x} \\\Leftrightarrow & 16x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 16x+3x& = &16-20 \\\Leftrightarrow & 19x& = &-4 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-4}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-4}{19} & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x+3)& = & -11 \color{red}{-} (8+x) \\\Leftrightarrow & 6x+6& = &-11-8-x \\\Leftrightarrow & 6x \color{red}{+6} & = &-19 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 6x+x& = &-19-6 \\\Leftrightarrow & 7x& = &-25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (2x-4)& = & 14 \color{red}{-} (1+x) \\\Leftrightarrow & 6x-12& = &14-1-x \\\Leftrightarrow & 6x \color{red}{-12} & = &13 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 6x+x& = &13+12 \\\Leftrightarrow & 7x& = &25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-6x+1)& = & 15 \color{red}{-} (15+x) \\\Leftrightarrow & -24x+4& = &15-15-x \\\Leftrightarrow & -24x \color{red}{+4} & = &0 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -24x+x& = &0-4 \\\Leftrightarrow & -23x& = &-4 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-4}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{4}{23} & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x-4)& = & 3 \color{red}{+} (-15+x) \\\Leftrightarrow & -3x-12& = &3-15+x \\\Leftrightarrow & -3x \color{red}{-12} & = &-12 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -3x-x& = &-12+12 \\\Leftrightarrow & -4x& = &0 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{0}{ \color{red}{-4} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x+4)& = & 11 \color{red}{-} (-2+x) \\\Leftrightarrow & -6x+24& = &11+2-x \\\Leftrightarrow & -6x \color{red}{+24} & = &13 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -6x+x& = &13-24 \\\Leftrightarrow & -5x& = &-11 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-11}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{11}{5} & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-2x-4)& = & -15 \color{red}{+} (12+x) \\\Leftrightarrow & -8x-16& = &-15+12+x \\\Leftrightarrow & -8x \color{red}{-16} & = &-3 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -8x-x& = &-3+16 \\\Leftrightarrow & -9x& = &13 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{13}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-13}{9} & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-2x+2)& = & -11 \color{red}{-} (11+3x) \\\Leftrightarrow & -8x+8& = &-11-11-3x \\\Leftrightarrow & -8x \color{red}{+8} & = &-22 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{+3x} & = &-22 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-8} \\\Leftrightarrow & -8x+3x& = &-22-8 \\\Leftrightarrow & -5x& = &-30 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-30}{ \color{red}{-5} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (4x-7)& = & -3 \color{red}{+} (-7+x) \\\Leftrightarrow & 20x-35& = &-3-7+x \\\Leftrightarrow & 20x \color{red}{-35} & = &-10 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+35} \\\Leftrightarrow & 20x-x& = &-10+35 \\\Leftrightarrow & 19x& = &25 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{25}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{25}{19} & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-3x-3)& = & 2 \color{red}{-} (13-5x) \\\Leftrightarrow & -18x-18& = &2-13+5x \\\Leftrightarrow & -18x \color{red}{-18} & = &-11 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -18x-5x& = &-11+18 \\\Leftrightarrow & -23x& = &7 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{7}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-7}{23} & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x+3)& = & 6 \color{red}{-} (-8+x) \\\Leftrightarrow & -24x+12& = &6+8-x \\\Leftrightarrow & -24x \color{red}{+12} & = &14 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &14-12 \\\Leftrightarrow & -23x& = &2 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{2}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x+5)& = & 14 \color{red}{+} (12+x) \\\Leftrightarrow & 24x+20& = &14+12+x \\\Leftrightarrow & 24x \color{red}{+20} & = &26 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 24x-x& = &26-20 \\\Leftrightarrow & 23x& = &6 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{6}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)