Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+5}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+11x } & = & 6 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &15x & = &1\\\Leftrightarrow & \color{red}{15}x & = &1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+14}& = & 2 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+3x } & = & 2 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 2 \color{blue}{-14} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-4}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4+11x } & = & 10 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &23x & = &14\\\Leftrightarrow & \color{red}{23}x & = &14\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{14}{23} \\\Leftrightarrow & \color{green}{ x = \frac{14}{23} } & & \\ & V = \left\{ \frac{14}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-13}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x } & = & 6 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{-12}& = & 5 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-9x } & = & 5 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-2x & = &17\\\Leftrightarrow & \color{red}{-2}x & = &17\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{17}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{2} } & & \\ & V = \left\{ \frac{-17}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-11}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x } & = & 14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{+11} \\\Leftrightarrow &-10x & = &25\\\Leftrightarrow & \color{red}{-10}x & = &25\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{25}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-18\\\Leftrightarrow & \color{red}{-5}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+1}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-x } & = & -14 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &-14x & = &-15\\\Leftrightarrow & \color{red}{-14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-4}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4-x } & = & 1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &13x & = &5\\\Leftrightarrow & \color{red}{13}x & = &5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-1}& = & 10 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1-9x } & = & 10 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &-5x & = &11\\\Leftrightarrow & \color{red}{-5}x & = &11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+8}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & -5 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-13\\\Leftrightarrow & \color{red}{-11}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{13}{11} } & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+10}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-5x } & = & -8 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)