Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+9}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-5x } & = & -2 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x } & = & -12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &-11x & = &-26\\\Leftrightarrow & \color{red}{-11}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{26}{11} } & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+11}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+11x } & = & 12 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 12 \color{blue}{-11} \\\Leftrightarrow &14x & = &1\\\Leftrightarrow & \color{red}{14}x & = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-9}& = & 1 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9+9x } & = & 1 \color{red}{ -9x }\color{blue}{+9+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & 1 \color{blue}{+9} \\\Leftrightarrow &16x & = &10\\\Leftrightarrow & \color{red}{16}x & = &10\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{10}{16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-x } & = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+6}& = & 7 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+7x } & = & 7 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &22x & = &1\\\Leftrightarrow & \color{red}{22}x & = &1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{22} } & & \\ & V = \left\{ \frac{1}{22} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-2}& = & 8 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2+15x } & = & 8 \color{red}{ -15x }\color{blue}{+2+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 8 \color{blue}{+2} \\\Leftrightarrow &23x & = &10\\\Leftrightarrow & \color{red}{23}x & = &10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-13}& = & 7 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13-2x } & = & 7 \color{red}{ +2x }\color{blue}{+13-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &3x & = &20\\\Leftrightarrow & \color{red}{3}x & = &20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+10}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x } & = & 7 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &-16x & = &-3\\\Leftrightarrow & \color{red}{-16}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{16} } & & \\ & V = \left\{ \frac{3}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-x } & = & -15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & 3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+2}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2-5x } & = & -14 \color{red}{ +5x }\color{blue}{-2-5x } \\\Leftrightarrow & -7x \color{blue}{-5x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)