Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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