Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+15}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-x } & = & 10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 10 \color{blue}{-15} \\\Leftrightarrow &-8x & = &-5\\\Leftrightarrow & \color{red}{-8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & 7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-8}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-x } & = & 13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &9x & = &21\\\Leftrightarrow & \color{red}{9}x & = &21\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{21}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+9}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9-11x } & = & -6 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &-21x & = &-15\\\Leftrightarrow & \color{red}{-21}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-15}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-x } & = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-x } & = & -2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &9x & = &-10\\\Leftrightarrow & \color{red}{9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-4}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-9x } & = & -5 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+5}& = & -6 \color{red}{ +4x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5-4x } & = & -6 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & 5x \color{blue}{-4x } & = & -6 \color{blue}{-5} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-x } & = & -12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -12 \color{blue}{+2} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12-x } & = & -6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+14}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14-5x } & = & -8 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &9x & = &-22\\\Leftrightarrow & \color{red}{9}x & = &-22\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-22}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-13}& = & -12 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-12x } & = & -12 \color{red}{ +12x }\color{blue}{+13-12x } \\\Leftrightarrow & -7x \color{blue}{-12x } & = & -12 \color{blue}{+13} \\\Leftrightarrow &-19x & = &1\\\Leftrightarrow & \color{red}{-19}x & = &1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{19} } & & \\ & V = \left\{ \frac{-1}{19} \right\} & \\\end{align}\)