Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+5}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & 6 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &-12x & = &1\\\Leftrightarrow & \color{red}{-12}x & = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9-x } & = & 4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &6x & = &-5\\\Leftrightarrow & \color{red}{6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-5}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x } & = & -7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &-15x & = &-14\\\Leftrightarrow & \color{red}{-15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+3}& = & 9 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3+6x } & = & 9 \color{red}{ -6x }\color{blue}{-3+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &19x & = &6\\\Leftrightarrow & \color{red}{19}x & = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-x } & = & 6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &-16x & = &16\\\Leftrightarrow & \color{red}{-16}x & = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+8}& = & -13 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-14x } & = & -13 \color{red}{ +14x }\color{blue}{-8-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &-27x & = &-21\\\Leftrightarrow & \color{red}{-27}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-21}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-3}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-11x } & = & -8 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-4}& = & -10 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4-2x } & = & -10 \color{red}{ +2x }\color{blue}{+4-2x } \\\Leftrightarrow & x \color{blue}{-2x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-4}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4-x } & = & -10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{+4} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+3}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-7x } & = & 14 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &-4x & = &11\\\Leftrightarrow & \color{red}{-4}x & = &11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+9}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9-7x } & = & -15 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &-6x & = &-24\\\Leftrightarrow & \color{red}{-6}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-24}{-6} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{+1}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-x } & = & -6 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &3x & = &-7\\\Leftrightarrow & \color{red}{3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)