Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x-1)& = & 10 \color{red}{+} (-8-2x) \\\Leftrightarrow & -9x-3& = &10-8-2x \\\Leftrightarrow & -9x \color{red}{-3} & = &2 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & -9x+2x& = &2+3 \\\Leftrightarrow & -7x& = &5 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{5}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-5}{7} & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-2x-7)& = & -4 \color{red}{+} (-5+3x) \\\Leftrightarrow & -8x-28& = &-4-5+3x \\\Leftrightarrow & -8x \color{red}{-28} & = &-9 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -8x-3x& = &-9+28 \\\Leftrightarrow & -11x& = &19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x-3)& = & 15 \color{red}{-} (-12+x) \\\Leftrightarrow & -6x-9& = &15+12-x \\\Leftrightarrow & -6x \color{red}{-9} & = &27 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & -6x+x& = &27+9 \\\Leftrightarrow & -5x& = &36 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{36}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-36}{5} & & \\ & V = \left\{ \frac{-36}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x-6)& = & -10 \color{red}{+} (6+x) \\\Leftrightarrow & 18x-36& = &-10+6+x \\\Leftrightarrow & 18x \color{red}{-36} & = &-4 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 18x-x& = &-4+36 \\\Leftrightarrow & 17x& = &32 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{32}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{32}{17} & & \\ & V = \left\{ \frac{32}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (4x-6)& = & -6 \color{red}{-} (-3+x) \\\Leftrightarrow & 12x-18& = &-6+3-x \\\Leftrightarrow & 12x \color{red}{-18} & = &-3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &-3+18 \\\Leftrightarrow & 13x& = &15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{15}{13} & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x+2)& = & -3 \color{red}{-} (-1-5x) \\\Leftrightarrow & 16x+8& = &-3+1+5x \\\Leftrightarrow & 16x \color{red}{+8} & = &-2 \color{red}{+5x} \\\Leftrightarrow & 16x \color{red}{+8} \color{blue}{-8} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-8} \\\Leftrightarrow & 16x-5x& = &-2-8 \\\Leftrightarrow & 11x& = &-10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-10}{11} & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x-4)& = & -13 \color{red}{+} (14+x) \\\Leftrightarrow & 12x-24& = &-13+14+x \\\Leftrightarrow & 12x \color{red}{-24} & = &1 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &1+24 \\\Leftrightarrow & 11x& = &25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{25}{11} & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-2x+1)& = & 13 \color{red}{+} (-8+3x) \\\Leftrightarrow & -4x+2& = &13-8+3x \\\Leftrightarrow & -4x \color{red}{+2} & = &5 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -4x-3x& = &5-2 \\\Leftrightarrow & -7x& = &3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x+7)& = & 11 \color{red}{+} (-7-3x) \\\Leftrightarrow & -4x+14& = &11-7-3x \\\Leftrightarrow & -4x \color{red}{+14} & = &4 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -4x+3x& = &4-14 \\\Leftrightarrow & -x& = &-10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-10}{ \color{red}{-1} } \\\Leftrightarrow & x = 10 & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x-2)& = & -13 \color{red}{+} (-14+3x) \\\Leftrightarrow & -20x-10& = &-13-14+3x \\\Leftrightarrow & -20x \color{red}{-10} & = &-27 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-27 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -20x-3x& = &-27+10 \\\Leftrightarrow & -23x& = &-17 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-17}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{17}{23} & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x-3)& = & -12 \color{red}{-} (-4-5x) \\\Leftrightarrow & 18x-18& = &-12+4+5x \\\Leftrightarrow & 18x \color{red}{-18} & = &-8 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & 18x-5x& = &-8+18 \\\Leftrightarrow & 13x& = &10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x-4)& = & 1 \color{red}{-} (-9+x) \\\Leftrightarrow & 24x-24& = &1+9-x \\\Leftrightarrow & 24x \color{red}{-24} & = &10 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 24x+x& = &10+24 \\\Leftrightarrow & 25x& = &34 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{34}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{34}{25} & & \\ & V = \left\{ \frac{34}{25} \right\} & \\\end{align}\)