Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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