Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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