Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+14}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-5x } & = & 5 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & 5 \color{blue}{-14} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+15}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-9x } & = & -8 \color{red}{ +9x }\color{blue}{-15-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-23\\\Leftrightarrow & \color{red}{-5}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-23}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{23}{5} } & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-2}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2-14x } & = & -4 \color{red}{ +14x }\color{blue}{+2-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -4 \color{blue}{+2} \\\Leftrightarrow &-27x & = &-2\\\Leftrightarrow & \color{red}{-27}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-2}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{2}{27} } & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+13}& = & 3 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13+12x } & = & 3 \color{red}{ -12x }\color{blue}{-13+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 3 \color{blue}{-13} \\\Leftrightarrow &17x & = &-10\\\Leftrightarrow & \color{red}{17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+14}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-9x } & = & -7 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &-17x & = &-21\\\Leftrightarrow & \color{red}{-17}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{21}{17} } & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-12}& = & -10 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+2x } & = & -10 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &17x & = &2\\\Leftrightarrow & \color{red}{17}x & = &2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{2}{17} } & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-3}& = & 2 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-9x } & = & 2 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-13x & = &5\\\Leftrightarrow & \color{red}{-13}x & = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-15}& = & -2 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+13x } & = & -2 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &20x & = &13\\\Leftrightarrow & \color{red}{20}x & = &13\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{13}{20} \\\Leftrightarrow & \color{green}{ x = \frac{13}{20} } & & \\ & V = \left\{ \frac{13}{20} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+10}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-13x } & = & -10 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -10 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-20\\\Leftrightarrow & \color{red}{-15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-9x & = &17\\\Leftrightarrow & \color{red}{-9}x & = &17\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{17}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{9} } & & \\ & V = \left\{ \frac{-17}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-5}& = & 10 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5+3x } & = & 10 \color{red}{ -3x }\color{blue}{+5+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &13x & = &15\\\Leftrightarrow & \color{red}{13}x & = &15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)