Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-9}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-4x } & = & 8 \color{red}{ +4x }\color{blue}{+9-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+12}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+12}\color{blue}{-12-x } & = & 9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{-12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x } & = & -7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-1}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1-5x } & = & 3 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &3x & = &4\\\Leftrightarrow & \color{red}{3}x & = &4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-9}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9+5x } & = & -8 \color{red}{ -5x }\color{blue}{+9+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -8 \color{blue}{+9} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-14}& = & 4 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14-6x } & = & 4 \color{red}{ +6x }\color{blue}{+14-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 4 \color{blue}{+14} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-x } & = & -14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+6}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-13x } & = & -7 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & -7 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{-8}& = & -13 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8-4x } & = & -13 \color{red}{ +4x }\color{blue}{+8-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &-x & = &-5\\\Leftrightarrow & \color{red}{-}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+10}& = & 4 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10+4x } & = & 4 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 4 \color{blue}{-10} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-x } & = & 2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-12x & = &14\\\Leftrightarrow & \color{red}{-12}x & = &14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-10}& = & -15 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10+8x } & = & -15 \color{red}{ -8x }\color{blue}{+10+8x } \\\Leftrightarrow & 3x \color{blue}{+8x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)