Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+7}& = & 11 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7-9x } & = & 11 \color{red}{ +9x }\color{blue}{-7-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &-2x & = &4\\\Leftrightarrow & \color{red}{-2}x & = &4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{4}{-2} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-8}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-8}\color{blue}{+8-11x } & = & 13 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &-3x & = &21\\\Leftrightarrow & \color{red}{-3}x & = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{-5}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5-10x } & = & 3 \color{red}{ +10x }\color{blue}{+5-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 3 \color{blue}{+5} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-13}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-9x } & = & 1 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 1 \color{blue}{+13} \\\Leftrightarrow &5x & = &14\\\Leftrightarrow & \color{red}{5}x & = &14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+8}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8+13x } & = & 4 \color{red}{ -13x }\color{blue}{-8+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &27x & = &-4\\\Leftrightarrow & \color{red}{27}x & = &-4\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-4}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{27} } & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+1}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-13x } & = & 13 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-19x & = &12\\\Leftrightarrow & \color{red}{-19}x & = &12\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{12}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10-x } & = & 3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &8x & = &-7\\\Leftrightarrow & \color{red}{8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-5}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5+13x } & = & 8 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &23x & = &13\\\Leftrightarrow & \color{red}{23}x & = &13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6-x } & = & -12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &13x & = &-18\\\Leftrightarrow & \color{red}{13}x & = &-18\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-18}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{13} } & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+15}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-13x } & = & -3 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+8}& = & 9 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8+4x } & = & 9 \color{red}{ -4x }\color{blue}{-8+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & 9 \color{blue}{-8} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-8}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8-7x } & = & -13 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)