Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-3}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-7x } & = & -10 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -10 \color{blue}{+3} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+10}& = & -13 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10+4x } & = & -13 \color{red}{ -4x }\color{blue}{-10+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &17x & = &-23\\\Leftrightarrow & \color{red}{17}x & = &-23\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-23}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{17} } & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+5}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-3x } & = & -11 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 7x \color{blue}{-3x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &4x & = &-16\\\Leftrightarrow & \color{red}{4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+7}& = & 7 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-5x } & = & 7 \color{red}{ +5x }\color{blue}{-7-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 7 \color{blue}{-7} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-12}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12-11x } & = & -5 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+15}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-13x } & = & -1 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &-19x & = &-16\\\Leftrightarrow & \color{red}{-19}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-16}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-8}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8-13x } & = & -15 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & x \color{blue}{-13x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+10}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+10}\color{blue}{-10-x } & = & -5 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &-15x & = &-15\\\Leftrightarrow & \color{red}{-15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+5}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-11x } & = & -15 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -15 \color{blue}{-5} \\\Leftrightarrow &-18x & = &-20\\\Leftrightarrow & \color{red}{-18}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-20}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+11}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11+7x } & = & -2 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &8x & = &-13\\\Leftrightarrow & \color{red}{8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-13}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+3}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-7x } & = & 4 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10-x } & = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 1 \color{blue}{-10} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)