Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+13}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13-14x } & = & 12 \color{red}{ +14x }\color{blue}{-13-14x } \\\Leftrightarrow & -x \color{blue}{-14x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+9}& = & -6 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9+14x } & = & -6 \color{red}{ -14x }\color{blue}{-9+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &17x & = &-15\\\Leftrightarrow & \color{red}{17}x & = &-15\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-15}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+15}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-11x } & = & -1 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &3x & = &-16\\\Leftrightarrow & \color{red}{3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-16}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{3} } & & \\ & V = \left\{ \frac{-16}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+10}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10-5x } & = & -8 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-5}& = & -9 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5+13x } & = & -9 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &23x & = &-4\\\Leftrightarrow & \color{red}{23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-3}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3+7x } & = & -3 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x } & = & -11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-14\\\Leftrightarrow & \color{red}{-5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+5}& = & 11 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5+9x } & = & 11 \color{red}{ -9x }\color{blue}{-5+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &19x & = &6\\\Leftrightarrow & \color{red}{19}x & = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & 6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 6 \color{blue}{-2} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-10}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10-3x } & = & 7 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &11x & = &17\\\Leftrightarrow & \color{red}{11}x & = &17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+2}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2+11x } & = & -13 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & x \color{blue}{+11x } & = & -13 \color{blue}{-2} \\\Leftrightarrow &12x & = &-15\\\Leftrightarrow & \color{red}{12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-15}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)