Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-1}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-x } & = & 12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{+1} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+11}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-5x } & = & -7 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -7 \color{blue}{-11} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+2}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2-11x } & = & 15 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & x \color{blue}{-11x } & = & 15 \color{blue}{-2} \\\Leftrightarrow &-10x & = &13\\\Leftrightarrow & \color{red}{-10}x & = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{-13}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-9x } & = & 6 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 6 \color{blue}{+13} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+6}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-5x } & = & 15 \color{red}{ +5x }\color{blue}{-6-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &-3x & = &9\\\Leftrightarrow & \color{red}{-3}x & = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+12}& = & 5 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12-12x } & = & 5 \color{red}{ +12x }\color{blue}{-12-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+4}& = & -5 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4+3x } & = & -5 \color{red}{ -3x }\color{blue}{-4+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+12}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-14x } & = & -5 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -5 \color{blue}{-12} \\\Leftrightarrow &-25x & = &-17\\\Leftrightarrow & \color{red}{-25}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-17}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{17}{25} } & & \\ & V = \left\{ \frac{17}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+10}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+10}\color{blue}{-10-x } & = & -13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &-14x & = &-23\\\Leftrightarrow & \color{red}{-14}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-23}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{23}{14} } & & \\ & V = \left\{ \frac{23}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-3}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x } & = & -6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -6 \color{blue}{+3} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+12}& = & 4 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12+2x } & = & 4 \color{red}{ -2x }\color{blue}{-12+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &x & = &-8\\\Leftrightarrow & \color{red}{}x & = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-12}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-13x } & = & -11 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &-28x & = &1\\\Leftrightarrow & \color{red}{-28}x & = &1\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{1}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{28} } & & \\ & V = \left\{ \frac{-1}{28} \right\} & \\\end{align}\)