Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x-3)& = & 1 \color{red}{+} (-14+x) \\\Leftrightarrow & 2x-6& = &1-14+x \\\Leftrightarrow & 2x \color{red}{-6} & = &-13 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 2x-x& = &-13+6 \\\Leftrightarrow & x& = &-7 \\ & V = \left\{ -7 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x-3)& = & -1 \color{red}{+} (9+x) \\\Leftrightarrow & -12x-12& = &-1+9+x \\\Leftrightarrow & -12x \color{red}{-12} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &8+12 \\\Leftrightarrow & -13x& = &20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x-7)& = & -15 \color{red}{-} (-7-5x) \\\Leftrightarrow & 6x-14& = &-15+7+5x \\\Leftrightarrow & 6x \color{red}{-14} & = &-8 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-14} \color{blue}{+14} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+14} \\\Leftrightarrow & 6x-5x& = &-8+14 \\\Leftrightarrow & x& = &6 \\ & V = \left\{ 6 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x-3)& = & -8 \color{red}{+} (13+x) \\\Leftrightarrow & 30x-18& = &-8+13+x \\\Leftrightarrow & 30x \color{red}{-18} & = &5 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 30x-x& = &5+18 \\\Leftrightarrow & 29x& = &23 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{23}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{23}{29} & & \\ & V = \left\{ \frac{23}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-4x+4)& = & 12 \color{red}{-} (14+x) \\\Leftrightarrow & -20x+20& = &12-14-x \\\Leftrightarrow & -20x \color{red}{+20} & = &-2 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -20x+x& = &-2-20 \\\Leftrightarrow & -19x& = &-22 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-22}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{22}{19} & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (3x-6)& = & 5 \color{red}{+} (11+2x) \\\Leftrightarrow & 9x-18& = &5+11+2x \\\Leftrightarrow & 9x \color{red}{-18} & = &16 \color{red}{+2x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{-2x} & = &16 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+18} \\\Leftrightarrow & 9x-2x& = &16+18 \\\Leftrightarrow & 7x& = &34 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{34}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{34}{7} & & \\ & V = \left\{ \frac{34}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-2x+6)& = & 6 \color{red}{+} (2-5x) \\\Leftrightarrow & -6x+18& = &6+2-5x \\\Leftrightarrow & -6x \color{red}{+18} & = &8 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -6x+5x& = &8-18 \\\Leftrightarrow & -x& = &-10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-10}{ \color{red}{-1} } \\\Leftrightarrow & x = 10 & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (3x+4)& = & -10 \color{red}{-} (11+x) \\\Leftrightarrow & 12x+16& = &-10-11-x \\\Leftrightarrow & 12x \color{red}{+16} & = &-21 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 12x+x& = &-21-16 \\\Leftrightarrow & 13x& = &-37 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-37}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-37}{13} & & \\ & V = \left\{ \frac{-37}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x+3)& = & -1 \color{red}{-} (-7+x) \\\Leftrightarrow & 16x+12& = &-1+7-x \\\Leftrightarrow & 16x \color{red}{+12} & = &6 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 16x+x& = &6-12 \\\Leftrightarrow & 17x& = &-6 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-6}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-6}{17} & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x-2)& = & 4 \color{red}{-} (-4+x) \\\Leftrightarrow & -24x-8& = &4+4-x \\\Leftrightarrow & -24x \color{red}{-8} & = &8 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -24x+x& = &8+8 \\\Leftrightarrow & -23x& = &16 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{16}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-16}{23} & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-4x-6)& = & 14 \color{red}{-} (-6+x) \\\Leftrightarrow & -24x-36& = &14+6-x \\\Leftrightarrow & -24x \color{red}{-36} & = &20 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -24x+x& = &20+36 \\\Leftrightarrow & -23x& = &56 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{56}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-56}{23} & & \\ & V = \left\{ \frac{-56}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x-4)& = & -1 \color{red}{+} (-12+x) \\\Leftrightarrow & -2x-8& = &-1-12+x \\\Leftrightarrow & -2x \color{red}{-8} & = &-13 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -2x-x& = &-13+8 \\\Leftrightarrow & -3x& = &-5 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-5}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{5}{3} & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)