Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-8}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8+13x } & = & 10 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &22x & = &18\\\Leftrightarrow & \color{red}{22}x & = &18\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{18}{22} \\\Leftrightarrow & \color{green}{ x = \frac{9}{11} } & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+5}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-8x } & = & 3 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+9}& = & 10 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9+3x } & = & 10 \color{red}{ -3x }\color{blue}{-9+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 10 \color{blue}{-9} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+10}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10-3x } & = & 4 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 4 \color{blue}{-10} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+7}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7-13x } & = & 3 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+4}& = & 8 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4+9x } & = & 8 \color{red}{ -9x }\color{blue}{-4+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &23x & = &4\\\Leftrightarrow & \color{red}{23}x & = &4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-10}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10-11x } & = & 10 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &-3x & = &20\\\Leftrightarrow & \color{red}{-3}x & = &20\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{20}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-1}& = & -12 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-4x } & = & -12 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &-19x & = &-11\\\Leftrightarrow & \color{red}{-19}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-11}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{11}{19} } & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{-4}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4-3x } & = & 7 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &7x & = &11\\\Leftrightarrow & \color{red}{7}x & = &11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-12}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12+13x } & = & 15 \color{red}{ -13x }\color{blue}{+12+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 15 \color{blue}{+12} \\\Leftrightarrow &23x & = &27\\\Leftrightarrow & \color{red}{23}x & = &27\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{27}{23} \\\Leftrightarrow & \color{green}{ x = \frac{27}{23} } & & \\ & V = \left\{ \frac{27}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-x } & = & -11 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &-9x & = &-16\\\Leftrightarrow & \color{red}{-9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8-x } & = & -8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -8 \color{blue}{-8} \\\Leftrightarrow &8x & = &-16\\\Leftrightarrow & \color{red}{8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-16}{8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)