Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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