Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(6(-5x-7)=6+(6+29x)\)
2. \(4(-2x-2)=-8-(-12+5x)\)
3. \(6(6x-6)=-3-(-9+5x)\)
4. \(5(5x-7)=-13-(6+2x)\)
5. \(4(-x+4)=-15+(-6+x)\)
6. \(6(4x-2)=-5+(4+x)\)
7. \(6(2x+5)=-15-(9+11x)\)
8. \(6(-4x+4)=-7+(-8+x)\)
9. \(5(-4x-5)=-2+(-2+3x)\)
10. \(6(-x-6)=15-(15+5x)\)
11. \(5(3x+5)=11+(-12-2x)\)
12. \(3(-6x-3)=-11+(12+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x-7)& = & 6 \color{red}{+} (6+29x) \\\Leftrightarrow & -30x-42& = &6+6+29x \\\Leftrightarrow & -30x \color{red}{-42} & = &12 \color{red}{+29x} \\\Leftrightarrow & -30x \color{red}{-42} \color{blue}{+42} \color{blue}{-29x} & = &12 \color{red}{+29x} \color{blue}{-29x} \color{blue}{+42} \\\Leftrightarrow & -30x-29x& = &12+42 \\\Leftrightarrow & -59x& = &54 \\\Leftrightarrow & \frac{-59x}{ \color{red}{-59} }& = &\frac{54}{ \color{red}{-59} } \\\Leftrightarrow & x = \frac{-54}{59} & & \\ & V = \left\{ \frac{-54}{59} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-2x-2)& = & -8 \color{red}{-} (-12+5x) \\\Leftrightarrow & -8x-8& = &-8+12-5x \\\Leftrightarrow & -8x \color{red}{-8} & = &4 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & -8x+5x& = &4+8 \\\Leftrightarrow & -3x& = &12 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{12}{ \color{red}{-3} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (6x-6)& = & -3 \color{red}{-} (-9+5x) \\\Leftrightarrow & 36x-36& = &-3+9-5x \\\Leftrightarrow & 36x \color{red}{-36} & = &6 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & 36x+5x& = &6+36 \\\Leftrightarrow & 41x& = &42 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{42}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{42}{41} & & \\ & V = \left\{ \frac{42}{41} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x-7)& = & -13 \color{red}{-} (6+2x) \\\Leftrightarrow & 25x-35& = &-13-6-2x \\\Leftrightarrow & 25x \color{red}{-35} & = &-19 \color{red}{-2x} \\\Leftrightarrow & 25x \color{red}{-35} \color{blue}{+35} \color{blue}{+2x} & = &-19 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+35} \\\Leftrightarrow & 25x+2x& = &-19+35 \\\Leftrightarrow & 27x& = &16 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = &\frac{16}{ \color{red}{27} } \\\Leftrightarrow & x = \frac{16}{27} & & \\ & V = \left\{ \frac{16}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x+4)& = & -15 \color{red}{+} (-6+x) \\\Leftrightarrow & -4x+16& = &-15-6+x \\\Leftrightarrow & -4x \color{red}{+16} & = &-21 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -4x-x& = &-21-16 \\\Leftrightarrow & -5x& = &-37 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-37}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{37}{5} & & \\ & V = \left\{ \frac{37}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x-2)& = & -5 \color{red}{+} (4+x) \\\Leftrightarrow & 24x-12& = &-5+4+x \\\Leftrightarrow & 24x \color{red}{-12} & = &-1 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &-1+12 \\\Leftrightarrow & 23x& = &11 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{11}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{11}{23} & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x+5)& = & -15 \color{red}{-} (9+11x) \\\Leftrightarrow & 12x+30& = &-15-9-11x \\\Leftrightarrow & 12x \color{red}{+30} & = &-24 \color{red}{-11x} \\\Leftrightarrow & 12x \color{red}{+30} \color{blue}{-30} \color{blue}{+11x} & = &-24 \color{red}{-11x} \color{blue}{+11x} \color{blue}{-30} \\\Leftrightarrow & 12x+11x& = &-24-30 \\\Leftrightarrow & 23x& = &-54 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-54}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-54}{23} & & \\ & V = \left\{ \frac{-54}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x+4)& = & -7 \color{red}{+} (-8+x) \\\Leftrightarrow & -24x+24& = &-7-8+x \\\Leftrightarrow & -24x \color{red}{+24} & = &-15 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -24x-x& = &-15-24 \\\Leftrightarrow & -25x& = &-39 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-39}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{39}{25} & & \\ & V = \left\{ \frac{39}{25} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x-5)& = & -2 \color{red}{+} (-2+3x) \\\Leftrightarrow & -20x-25& = &-2-2+3x \\\Leftrightarrow & -20x \color{red}{-25} & = &-4 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &-4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & -20x-3x& = &-4+25 \\\Leftrightarrow & -23x& = &21 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{21}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-21}{23} & & \\ & V = \left\{ \frac{-21}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-x-6)& = & 15 \color{red}{-} (15+5x) \\\Leftrightarrow & -6x-36& = &15-15-5x \\\Leftrightarrow & -6x \color{red}{-36} & = &0 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+36} \\\Leftrightarrow & -6x+5x& = &0+36 \\\Leftrightarrow & -x& = &36 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{36}{ \color{red}{-1} } \\\Leftrightarrow & x = -36 & & \\ & V = \left\{ -36 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (3x+5)& = & 11 \color{red}{+} (-12-2x) \\\Leftrightarrow & 15x+25& = &11-12-2x \\\Leftrightarrow & 15x \color{red}{+25} & = &-1 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+25} \color{blue}{-25} \color{blue}{+2x} & = &-1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-25} \\\Leftrightarrow & 15x+2x& = &-1-25 \\\Leftrightarrow & 17x& = &-26 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-26}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-26}{17} & & \\ & V = \left\{ \frac{-26}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-6x-3)& = & -11 \color{red}{+} (12+x) \\\Leftrightarrow & -18x-9& = &-11+12+x \\\Leftrightarrow & -18x \color{red}{-9} & = &1 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -18x-x& = &1+9 \\\Leftrightarrow & -19x& = &10 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{10}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-10}{19} & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)