Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+13}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-x } & = & 9 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-10x & = &18\\\Leftrightarrow & \color{red}{-10}x & = &18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+4}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+4}\color{blue}{-4-7x } & = & -9 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & -9 \color{blue}{-4} \\\Leftrightarrow &-10x & = &-13\\\Leftrightarrow & \color{red}{-10}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{10} } & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-10}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-10}\color{blue}{+10-11x } & = & 15 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-13x & = &25\\\Leftrightarrow & \color{red}{-13}x & = &25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-4}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-4x } & = & 5 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+10}& = & -9 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10+15x } & = & -9 \color{red}{ -15x }\color{blue}{-10+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &19x & = &-19\\\Leftrightarrow & \color{red}{19}x & = &-19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-19}{19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+9}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-11x } & = & -6 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -13x \color{blue}{-11x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &-24x & = &-15\\\Leftrightarrow & \color{red}{-24}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}} & = & \frac{-15}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15-x } & = & -5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &-16x & = &-20\\\Leftrightarrow & \color{red}{-16}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-20}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+1}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & 12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-4}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-x } & = & 11 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &12x & = &15\\\Leftrightarrow & \color{red}{12}x & = &15\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{15}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-x } & = & -5 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)