Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+4}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & -9 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -9 \color{blue}{-4} \\\Leftrightarrow &-14x & = &-13\\\Leftrightarrow & \color{red}{-14}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-10}& = & 10 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10+3x } & = & 10 \color{red}{ -3x }\color{blue}{+10+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & 10 \color{blue}{+10} \\\Leftrightarrow &16x & = &20\\\Leftrightarrow & \color{red}{16}x & = &20\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{20}{16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-x } & = & 10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{-12} \\\Leftrightarrow &-12x & = &-2\\\Leftrightarrow & \color{red}{-12}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x } & = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-x } & = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -9 \color{blue}{-5} \\\Leftrightarrow &11x & = &-14\\\Leftrightarrow & \color{red}{11}x & = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-1}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-x } & = & -8 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &-14x & = &-7\\\Leftrightarrow & \color{red}{-14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-10}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10+7x } & = & -13 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &22x & = &-3\\\Leftrightarrow & \color{red}{22}x & = &-3\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-3}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{22} } & & \\ & V = \left\{ \frac{-3}{22} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+3}& = & -9 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-4x } & = & -9 \color{red}{ +4x }\color{blue}{-3-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -9 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+14}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-7x } & = & 2 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{-11}& = & 6 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+13x } & = & 6 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 6 \color{blue}{+11} \\\Leftrightarrow &22x & = &17\\\Leftrightarrow & \color{red}{22}x & = &17\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{17}{22} \\\Leftrightarrow & \color{green}{ x = \frac{17}{22} } & & \\ & V = \left\{ \frac{17}{22} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-13}\color{blue}{+13-x } & = & 4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &-10x & = &17\\\Leftrightarrow & \color{red}{-10}x & = &17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & -13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &-12x & = &-15\\\Leftrightarrow & \color{red}{-12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)