Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+3}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x } & = & -7 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{-3} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-x } & = & -6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &11x & = &3\\\Leftrightarrow & \color{red}{11}x & = &3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-15}& = & -14 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+10x } & = & -14 \color{red}{ -10x }\color{blue}{+15+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &17x & = &1\\\Leftrightarrow & \color{red}{17}x & = &1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+7}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-3x } & = & 10 \color{red}{ +3x }\color{blue}{-7-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & 12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &-15x & = &23\\\Leftrightarrow & \color{red}{-15}x & = &23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{15} } & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{+10}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-13x } & = & 15 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &-28x & = &5\\\Leftrightarrow & \color{red}{-28}x & = &5\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{5}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{28} } & & \\ & V = \left\{ \frac{-5}{28} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x } & = & -8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &-10x & = &-23\\\Leftrightarrow & \color{red}{-10}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-23}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{23}{10} } & & \\ & V = \left\{ \frac{23}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-x } & = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 13 \color{blue}{+5} \\\Leftrightarrow &-7x & = &18\\\Leftrightarrow & \color{red}{-7}x & = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+5}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5-13x } & = & -8 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &-25x & = &-13\\\Leftrightarrow & \color{red}{-25}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-13}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{13}{25} } & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-x } & = & -7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &5x & = &-8\\\Leftrightarrow & \color{red}{5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-2}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & 7 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 7 \color{blue}{+2} \\\Leftrightarrow &-8x & = &9\\\Leftrightarrow & \color{red}{-8}x & = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-8}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-3x } & = & 4 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &7x & = &12\\\Leftrightarrow & \color{red}{7}x & = &12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)