Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-9}& = & -10 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9+7x } & = & -10 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &15x & = &-1\\\Leftrightarrow & \color{red}{15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x } & = & -7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &-9x & = &-21\\\Leftrightarrow & \color{red}{-9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7-x } & = & -14 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+4}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-x } & = & 1 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &-12x & = &-3\\\Leftrightarrow & \color{red}{-12}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+10}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10-5x } & = & -2 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x } & = & -11 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-20\\\Leftrightarrow & \color{red}{-7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-20}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+6}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-7x } & = & 1 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 1 \color{blue}{-6} \\\Leftrightarrow &3x & = &-5\\\Leftrightarrow & \color{red}{3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+3}& = & 5 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-8x } & = & 5 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-21x & = &2\\\Leftrightarrow & \color{red}{-21}x & = &2\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{2}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{21} } & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & 2 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 2 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{+6}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-7x } & = & -13 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & -13 \color{blue}{-6} \\\Leftrightarrow &-16x & = &-19\\\Leftrightarrow & \color{red}{-16}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-19}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{19}{16} } & & \\ & V = \left\{ \frac{19}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+6}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6-7x } & = & 11 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &5x & = &5\\\Leftrightarrow & \color{red}{5}x & = &5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{5}{5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{-1}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1-3x } & = & -11 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)