Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+9}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+7}& = & 11 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7+2x } & = & 11 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &7x & = &4\\\Leftrightarrow & \color{red}{7}x & = &4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-1}& = & 1 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1-4x } & = & 1 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 1 \color{blue}{+1} \\\Leftrightarrow &-x & = &2\\\Leftrightarrow & \color{red}{-}x & = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+8}& = & 2 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8+6x } & = & 2 \color{red}{ -6x }\color{blue}{-8+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 2 \color{blue}{-8} \\\Leftrightarrow &19x & = &-6\\\Leftrightarrow & \color{red}{19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{19} } & & \\ & V = \left\{ \frac{-6}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-x } & = & 13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-4x & = &23\\\Leftrightarrow & \color{red}{-4}x & = &23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{4} } & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 9x \color{red}{+14}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14-10x } & = & 3 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 3 \color{blue}{-14} \\\Leftrightarrow &-x & = &-11\\\Leftrightarrow & \color{red}{-}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-11}{-1} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+1}& = & -14 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1-4x } & = & -14 \color{red}{ +4x }\color{blue}{-1-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & -14 \color{blue}{-1} \\\Leftrightarrow &9x & = &-15\\\Leftrightarrow & \color{red}{9}x & = &-15\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-15}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+11}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-7x } & = & -9 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-20\\\Leftrightarrow & \color{red}{-13}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-20}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{-12}& = & 10 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-12x } & = & 10 \color{red}{ +12x }\color{blue}{+12-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &-13x & = &22\\\Leftrightarrow & \color{red}{-13}x & = &22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-x } & = & -2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-10\\\Leftrightarrow & \color{red}{-7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-6}& = & 2 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-4x } & = & 2 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)