Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (6x+1)& = & -6 \color{red}{+} (-8-5x) \\\Leftrightarrow & 36x+6& = &-6-8-5x \\\Leftrightarrow & 36x \color{red}{+6} & = &-14 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 36x+5x& = &-14-6 \\\Leftrightarrow & 41x& = &-20 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-20}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-20}{41} & & \\ & V = \left\{ \frac{-20}{41} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x+6)& = & -1 \color{red}{-} (-1+x) \\\Leftrightarrow & 24x+36& = &-1+1-x \\\Leftrightarrow & 24x \color{red}{+36} & = &0 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 24x+x& = &0-36 \\\Leftrightarrow & 25x& = &-36 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-36}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-36}{25} & & \\ & V = \left\{ \frac{-36}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x-3)& = & -5 \color{red}{+} (4+x) \\\Leftrightarrow & -18x-9& = &-5+4+x \\\Leftrightarrow & -18x \color{red}{-9} & = &-1 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -18x-x& = &-1+9 \\\Leftrightarrow & -19x& = &8 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{8}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-8}{19} & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x+6)& = & 4 \color{red}{-} (7+3x) \\\Leftrightarrow & -4x+24& = &4-7-3x \\\Leftrightarrow & -4x \color{red}{+24} & = &-3 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{+3x} & = &-3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-24} \\\Leftrightarrow & -4x+3x& = &-3-24 \\\Leftrightarrow & -x& = &-27 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-27}{ \color{red}{-1} } \\\Leftrightarrow & x = 27 & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-3x+7)& = & -9 \color{red}{+} (3+x) \\\Leftrightarrow & -12x+28& = &-9+3+x \\\Leftrightarrow & -12x \color{red}{+28} & = &-6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -12x-x& = &-6-28 \\\Leftrightarrow & -13x& = &-34 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-34}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{34}{13} & & \\ & V = \left\{ \frac{34}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-2x-5)& = & -9 \color{red}{+} (15-5x) \\\Leftrightarrow & -6x-15& = &-9+15-5x \\\Leftrightarrow & -6x \color{red}{-15} & = &6 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & -6x+5x& = &6+15 \\\Leftrightarrow & -x& = &21 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{21}{ \color{red}{-1} } \\\Leftrightarrow & x = -21 & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-4x+3)& = & -5 \color{red}{-} (3+x) \\\Leftrightarrow & -12x+9& = &-5-3-x \\\Leftrightarrow & -12x \color{red}{+9} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -12x+x& = &-8-9 \\\Leftrightarrow & -11x& = &-17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (x+4)& = & -13 \color{red}{-} (8+x) \\\Leftrightarrow & 2x+8& = &-13-8-x \\\Leftrightarrow & 2x \color{red}{+8} & = &-21 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 2x+x& = &-21-8 \\\Leftrightarrow & 3x& = &-29 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-29}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-29}{3} & & \\ & V = \left\{ \frac{-29}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (3x-3)& = & 8 \color{red}{+} (-2-5x) \\\Leftrightarrow & 6x-6& = &8-2-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &6 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &6+6 \\\Leftrightarrow & 11x& = &12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{12}{11} & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x-2)& = & 6 \color{red}{+} (-7-4x) \\\Leftrightarrow & -9x-6& = &6-7-4x \\\Leftrightarrow & -9x \color{red}{-6} & = &-1 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &-1 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & -9x+4x& = &-1+6 \\\Leftrightarrow & -5x& = &5 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{5}{ \color{red}{-5} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x-1)& = & 1 \color{red}{+} (-4+x) \\\Leftrightarrow & 30x-6& = &1-4+x \\\Leftrightarrow & 30x \color{red}{-6} & = &-3 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 30x-x& = &-3+6 \\\Leftrightarrow & 29x& = &3 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{3}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{3}{29} & & \\ & V = \left\{ \frac{3}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x+7)& = & -8 \color{red}{+} (-11+x) \\\Leftrightarrow & -20x+28& = &-8-11+x \\\Leftrightarrow & -20x \color{red}{+28} & = &-19 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -20x-x& = &-19-28 \\\Leftrightarrow & -21x& = &-47 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-47}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{47}{21} & & \\ & V = \left\{ \frac{47}{21} \right\} & \\\end{align}\)