Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-x } & = & -5 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{-1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-x } & = & -9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &-12x & = &-8\\\Leftrightarrow & \color{red}{-12}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+1}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & -2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+9}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9+11x } & = & -13 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &17x & = &-22\\\Leftrightarrow & \color{red}{17}x & = &-22\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-22}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{17} } & & \\ & V = \left\{ \frac{-22}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{-10}& = & -3 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-10}\color{blue}{+10+2x } & = & -3 \color{red}{ -2x }\color{blue}{+10+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-x } & = & -9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &-16x & = &-10\\\Leftrightarrow & \color{red}{-16}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+14}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-x } & = & 11 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+9}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9+13x } & = & 3 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 3 \color{blue}{-9} \\\Leftrightarrow &22x & = &-6\\\Leftrightarrow & \color{red}{22}x & = &-6\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-6}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12-x } & = & -11 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -11 \color{blue}{+12} \\\Leftrightarrow &11x & = &1\\\Leftrightarrow & \color{red}{11}x & = &1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-5}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-5x } & = & 13 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-9x & = &18\\\Leftrightarrow & \color{red}{-9}x & = &18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{18}{-9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-7}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-8x } & = & -8 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &-21x & = &-1\\\Leftrightarrow & \color{red}{-21}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-1}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{1}{21} } & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+9}& = & 2 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9+14x } & = & 2 \color{red}{ -14x }\color{blue}{-9+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &17x & = &-7\\\Leftrightarrow & \color{red}{17}x & = &-7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)