Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+5}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+11x } & = & -3 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -3 \color{blue}{-5} \\\Leftrightarrow &15x & = &-8\\\Leftrightarrow & \color{red}{15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14-x } & = & -2 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &-16x & = &-16\\\Leftrightarrow & \color{red}{-16}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-16}{-16} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+6}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6-7x } & = & -9 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &-20x & = &-15\\\Leftrightarrow & \color{red}{-20}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-15}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+14}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-8x } & = & 13 \color{red}{ +8x }\color{blue}{-14-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+11}& = & -15 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11-6x } & = & -15 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &7x & = &-26\\\Leftrightarrow & \color{red}{7}x & = &-26\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-26}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{7} } & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-8}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-8}\color{blue}{+8+11x } & = & -13 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{-2}& = & 1 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-2}\color{blue}{+2+11x } & = & 1 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 1 \color{blue}{+2} \\\Leftrightarrow &15x & = &3\\\Leftrightarrow & \color{red}{15}x & = &3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-9}& = & 6 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+7x } & = & 6 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &22x & = &15\\\Leftrightarrow & \color{red}{22}x & = &15\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{15}{22} \\\Leftrightarrow & \color{green}{ x = \frac{15}{22} } & & \\ & V = \left\{ \frac{15}{22} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3-x } & = & -9 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{+10}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-x } & = & 3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &-6x & = &-7\\\Leftrightarrow & \color{red}{-6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+14}& = & 12 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14+2x } & = & 12 \color{red}{ -2x }\color{blue}{-14+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5-x } & = & -8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -8 \color{blue}{-5} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)