Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-9}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9-x } & = & -4 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -4 \color{blue}{+9} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-7}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-13x } & = & 10 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 10 \color{blue}{+7} \\\Leftrightarrow &-28x & = &17\\\Leftrightarrow & \color{red}{-28}x & = &17\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{17}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{28} } & & \\ & V = \left\{ \frac{-17}{28} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{-11}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+7x } & = & -12 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &8x & = &-1\\\Leftrightarrow & \color{red}{8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+3}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-x } & = & 5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & -1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -1 \color{blue}{+14} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-1}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-13x } & = & 10 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & 10 \color{blue}{+1} \\\Leftrightarrow &-25x & = &11\\\Leftrightarrow & \color{red}{-25}x & = &11\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{11}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{25} } & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & -15x \color{red}{-9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-x } & = & -7 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+5}& = & -15 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5+14x } & = & -15 \color{red}{ -14x }\color{blue}{-5+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &29x & = &-20\\\Leftrightarrow & \color{red}{29}x & = &-20\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{-20}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{29} } & & \\ & V = \left\{ \frac{-20}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+3}& = & -2 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3+15x } & = & -2 \color{red}{ -15x }\color{blue}{-3+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -2 \color{blue}{-3} \\\Leftrightarrow &19x & = &-5\\\Leftrightarrow & \color{red}{19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+3}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x } & = & 4 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &-13x & = &1\\\Leftrightarrow & \color{red}{-13}x & = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+9}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9-3x } & = & 14 \color{red}{ +3x }\color{blue}{-9-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 14 \color{blue}{-9} \\\Leftrightarrow &2x & = &5\\\Leftrightarrow & \color{red}{2}x & = &5\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{5}{2} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-x } & = & -4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &-12x & = &-16\\\Leftrightarrow & \color{red}{-12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)