Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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