Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x } & = & -12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &-8x & = &2\\\Leftrightarrow & \color{red}{-8}x & = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-9}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-11x } & = & 2 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 2 \color{blue}{+9} \\\Leftrightarrow &-21x & = &11\\\Leftrightarrow & \color{red}{-21}x & = &11\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{11}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{21} } & & \\ & V = \left\{ \frac{-11}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-6}\color{blue}{+6-x } & = & 3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+10}& = & 5 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10+13x } & = & 5 \color{red}{ -13x }\color{blue}{-10+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &22x & = &-5\\\Leftrightarrow & \color{red}{22}x & = &-5\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-5}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{22} } & & \\ & V = \left\{ \frac{-5}{22} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-6}& = & -7 \color{red}{ -5x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6+5x } & = & -7 \color{red}{ -5x }\color{blue}{+6+5x } \\\Leftrightarrow & -x \color{blue}{+5x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &4x & = &-1\\\Leftrightarrow & \color{red}{4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+5}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-9x } & = & 12 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &-13x & = &7\\\Leftrightarrow & \color{red}{-13}x & = &7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+6}& = & 6 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6-11x } & = & 6 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & 6 \color{blue}{-6} \\\Leftrightarrow &4x & = &0\\\Leftrightarrow & \color{red}{4}x & = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-13}& = & -13 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-9x } & = & -13 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+9}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-5x } & = & 2 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 3x \color{blue}{-5x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-2x & = &-7\\\Leftrightarrow & \color{red}{-2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-5}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & 1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-12}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12+13x } & = & 14 \color{red}{ -13x }\color{blue}{+12+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 14 \color{blue}{+12} \\\Leftrightarrow &24x & = &26\\\Leftrightarrow & \color{red}{24}x & = &26\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{26}{24} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-3}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-8x } & = & 12 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & 12 \color{blue}{+3} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)