Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+4}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4+11x } & = & -2 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &17x & = &-6\\\Leftrightarrow & \color{red}{17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-1}& = & -13 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+8x } & = & -13 \color{red}{ -8x }\color{blue}{+1+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &9x & = &-12\\\Leftrightarrow & \color{red}{9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 9x \color{red}{+5}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5-x } & = & -10 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -10 \color{blue}{-5} \\\Leftrightarrow &8x & = &-15\\\Leftrightarrow & \color{red}{8}x & = &-15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-9}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9-11x } & = & -7 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-10}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10+7x } & = & 12 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &22x & = &22\\\Leftrightarrow & \color{red}{22}x & = &22\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{22}{22} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-12}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12-x } & = & -1 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -1 \color{blue}{+12} \\\Leftrightarrow &9x & = &11\\\Leftrightarrow & \color{red}{9}x & = &11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-15}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{-15}\color{blue}{+15-13x } & = & -7 \color{red}{ +13x }\color{blue}{+15-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & -7 \color{blue}{+15} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-x } & = & -1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-16x & = &-14\\\Leftrightarrow & \color{red}{-16}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-9}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x } & = & 3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-6x & = &12\\\Leftrightarrow & \color{red}{-6}x & = &12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{12}{-6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+10}& = & 10 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10-4x } & = & 10 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 10 \color{blue}{-10} \\\Leftrightarrow &-x & = &0\\\Leftrightarrow & \color{red}{-}x & = &0\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{0}{-1} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+11}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-13x } & = & 6 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+9}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x } & = & 2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)