Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+14}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14-7x } & = & 14 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-x } & = & 7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-11}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11-x } & = & -7 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-10}& = & 7 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10-2x } & = & 7 \color{red}{ +2x }\color{blue}{+10-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &-x & = &17\\\Leftrightarrow & \color{red}{-}x & = &17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{17}{-1} \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+10}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-3x } & = & 3 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{-2}& = & -9 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-10x } & = & -9 \color{red}{ +10x }\color{blue}{+2-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-x } & = & -13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-10x & = &-4\\\Leftrightarrow & \color{red}{-10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+5}& = & -1 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5-8x } & = & -1 \color{red}{ +8x }\color{blue}{-5-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & -11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-15\\\Leftrightarrow & \color{red}{-7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9-x } & = & 12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &-8x & = &21\\\Leftrightarrow & \color{red}{-8}x & = &21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-4}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4+11x } & = & 3 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 3 \color{blue}{+4} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+9}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9-x } & = & -4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)