Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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