Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-x } & = & -10 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -10 \color{blue}{+1} \\\Leftrightarrow &-14x & = &-9\\\Leftrightarrow & \color{red}{-14}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+8}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8-x } & = & 12 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & 13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-8x & = &12\\\Leftrightarrow & \color{red}{-8}x & = &12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+2}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-9x } & = & 13 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-15}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15-x } & = & 14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 14 \color{blue}{+15} \\\Leftrightarrow &-15x & = &29\\\Leftrightarrow & \color{red}{-15}x & = &29\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{29}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{15} } & & \\ & V = \left\{ \frac{-29}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+6}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6+13x } & = & 14 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 14 \color{blue}{-6} \\\Leftrightarrow &21x & = &8\\\Leftrightarrow & \color{red}{21}x & = &8\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{8}{21} \\\Leftrightarrow & \color{green}{ x = \frac{8}{21} } & & \\ & V = \left\{ \frac{8}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-13}& = & -8 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-8x } & = & -8 \color{red}{ +8x }\color{blue}{+13-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{-5}& = & 10 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-13x } & = & 10 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &-17x & = &15\\\Leftrightarrow & \color{red}{-17}x & = &15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+7}& = & -6 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7+2x } & = & -6 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 13x \color{blue}{+2x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &15x & = &-13\\\Leftrightarrow & \color{red}{15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-9}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9-x } & = & 12 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &-15x & = &21\\\Leftrightarrow & \color{red}{-15}x & = &21\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{21}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-x } & = & 1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-4x & = &9\\\Leftrightarrow & \color{red}{-4}x & = &9\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{9}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-x } & = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 14 \color{blue}{-12} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)