Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-7}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7-11x } & = & -15 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{+5}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5+7x } & = & -13 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -13 \color{blue}{-5} \\\Leftrightarrow &19x & = &-18\\\Leftrightarrow & \color{red}{19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-18}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x } & = & 7 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 7 \color{blue}{+3} \\\Leftrightarrow &-11x & = &10\\\Leftrightarrow & \color{red}{-11}x & = &10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-8}& = & 5 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8+8x } & = & 5 \color{red}{ -8x }\color{blue}{+8+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & 5 \color{blue}{+8} \\\Leftrightarrow &9x & = &13\\\Leftrightarrow & \color{red}{9}x & = &13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+11}& = & -8 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11-15x } & = & -8 \color{red}{ +15x }\color{blue}{-11-15x } \\\Leftrightarrow & x \color{blue}{-15x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-14x & = &-19\\\Leftrightarrow & \color{red}{-14}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-x } & = & 7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & 1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &-6x & = &11\\\Leftrightarrow & \color{red}{-6}x & = &11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+10}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-x } & = & 9 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{-10} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{+7}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-7x } & = & 1 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x } & = & -6 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x } & = & 9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-16x & = &11\\\Leftrightarrow & \color{red}{-16}x & = &11\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{11}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{-9}& = & 6 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9+15x } & = & 6 \color{red}{ -15x }\color{blue}{+9+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &28x & = &15\\\Leftrightarrow & \color{red}{28}x & = &15\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{15}{28} \\\Leftrightarrow & \color{green}{ x = \frac{15}{28} } & & \\ & V = \left\{ \frac{15}{28} \right\} & \\\end{align}\)