Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-5}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+11x } & = & 13 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &17x & = &18\\\Leftrightarrow & \color{red}{17}x & = &18\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{18}{17} \\\Leftrightarrow & \color{green}{ x = \frac{18}{17} } & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+11}& = & -4 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+3x } & = & -4 \color{red}{ -3x }\color{blue}{-11+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &7x & = &-15\\\Leftrightarrow & \color{red}{7}x & = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+8}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8-x } & = & -5 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &-16x & = &-13\\\Leftrightarrow & \color{red}{-16}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-13}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{13}{16} } & & \\ & V = \left\{ \frac{13}{16} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-7}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-3x } & = & 15 \color{red}{ +3x }\color{blue}{+7-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &2x & = &22\\\Leftrightarrow & \color{red}{2}x & = &22\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{22}{2} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-6}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-6}\color{blue}{+6-x } & = & -4 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -4 \color{blue}{+6} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+3}& = & 14 \color{red}{ +8x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3-8x } & = & 14 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & 5x \color{blue}{-8x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-12}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-8x } & = & -3 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &-x & = &9\\\Leftrightarrow & \color{red}{-}x & = &9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{9}{-1} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-x } & = & 7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{-3} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-1}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1-3x } & = & 14 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 11x \color{blue}{-3x } & = & 14 \color{blue}{+1} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-1}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1-10x } & = & -8 \color{red}{ +10x }\color{blue}{+1-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &-19x & = &-7\\\Leftrightarrow & \color{red}{-19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-12}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-9x } & = & 7 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & x \color{blue}{-9x } & = & 7 \color{blue}{+12} \\\Leftrightarrow &-8x & = &19\\\Leftrightarrow & \color{red}{-8}x & = &19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{+4}& = & 1 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4+7x } & = & 1 \color{red}{ -7x }\color{blue}{-4+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &15x & = &-3\\\Leftrightarrow & \color{red}{15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)