Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+4}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4-13x } & = & 14 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 4x \color{blue}{-13x } & = & 14 \color{blue}{-4} \\\Leftrightarrow &-9x & = &10\\\Leftrightarrow & \color{red}{-9}x & = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x } & = & 5 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+9}& = & 13 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-14x } & = & 13 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 13 \color{blue}{-9} \\\Leftrightarrow &-25x & = &4\\\Leftrightarrow & \color{red}{-25}x & = &4\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{4}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{25} } & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-12}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12-13x } & = & 13 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 2x \color{blue}{-13x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &-11x & = &25\\\Leftrightarrow & \color{red}{-11}x & = &25\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{25}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{11} } & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-12}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12-x } & = & -8 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -8 \color{blue}{+12} \\\Leftrightarrow &2x & = &4\\\Leftrightarrow & \color{red}{2}x & = &4\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{4}{2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-8}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8-8x } & = & -2 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-10}& = & 4 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-14x } & = & 4 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &-27x & = &14\\\Leftrightarrow & \color{red}{-27}x & = &14\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{14}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{27} } & & \\ & V = \left\{ \frac{-14}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-13}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-x } & = & -13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -13 \color{blue}{+13} \\\Leftrightarrow &9x & = &0\\\Leftrightarrow & \color{red}{9}x & = &0\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{0}{9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-x } & = & -6 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+1}& = & 1 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+6x } & = & 1 \color{red}{ -6x }\color{blue}{-1+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-15}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-x } & = & 4 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-8x & = &19\\\Leftrightarrow & \color{red}{-8}x & = &19\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{19}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{8} } & & \\ & V = \left\{ \frac{-19}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-12}& = & -5 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+2x } & = & -5 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &17x & = &7\\\Leftrightarrow & \color{red}{17}x & = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)