Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-6x+1)& = & -14 \color{red}{+} (4+x) \\\Leftrightarrow & -24x+4& = &-14+4+x \\\Leftrightarrow & -24x \color{red}{+4} & = &-10 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -24x-x& = &-10-4 \\\Leftrightarrow & -25x& = &-14 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-14}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{14}{25} & & \\ & V = \left\{ \frac{14}{25} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x-5)& = & -9 \color{red}{-} (3+x) \\\Leftrightarrow & 24x-30& = &-9-3-x \\\Leftrightarrow & 24x \color{red}{-30} & = &-12 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 24x+x& = &-12+30 \\\Leftrightarrow & 25x& = &18 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{18}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{18}{25} & & \\ & V = \left\{ \frac{18}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-6x+6)& = & 4 \color{red}{-} (-15-5x) \\\Leftrightarrow & -36x+36& = &4+15+5x \\\Leftrightarrow & -36x \color{red}{+36} & = &19 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{-5x} & = &19 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-36} \\\Leftrightarrow & -36x-5x& = &19-36 \\\Leftrightarrow & -41x& = &-17 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-17}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{17}{41} & & \\ & V = \left\{ \frac{17}{41} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x+2)& = & 1 \color{red}{+} (-4+x) \\\Leftrightarrow & -20x+8& = &1-4+x \\\Leftrightarrow & -20x \color{red}{+8} & = &-3 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -20x-x& = &-3-8 \\\Leftrightarrow & -21x& = &-11 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-11}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{11}{21} & & \\ & V = \left\{ \frac{11}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x+1)& = & 15 \color{red}{+} (2-5x) \\\Leftrightarrow & -18x+6& = &15+2-5x \\\Leftrightarrow & -18x \color{red}{+6} & = &17 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -18x+5x& = &17-6 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-2x+2)& = & -3 \color{red}{-} (7+x) \\\Leftrightarrow & -8x+8& = &-3-7-x \\\Leftrightarrow & -8x \color{red}{+8} & = &-10 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -8x+x& = &-10-8 \\\Leftrightarrow & -7x& = &-18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{18}{7} & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x+7)& = & -5 \color{red}{+} (10+2x) \\\Leftrightarrow & -15x+21& = &-5+10+2x \\\Leftrightarrow & -15x \color{red}{+21} & = &5 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & -15x-2x& = &5-21 \\\Leftrightarrow & -17x& = &-16 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-16}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{16}{17} & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (6x+4)& = & -2 \color{red}{+} (-3+x) \\\Leftrightarrow & 30x+20& = &-2-3+x \\\Leftrightarrow & 30x \color{red}{+20} & = &-5 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 30x-x& = &-5-20 \\\Leftrightarrow & 29x& = &-25 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-25}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-25}{29} & & \\ & V = \left\{ \frac{-25}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x+6)& = & -5 \color{red}{-} (-10+x) \\\Leftrightarrow & 24x+36& = &-5+10-x \\\Leftrightarrow & 24x \color{red}{+36} & = &5 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 24x+x& = &5-36 \\\Leftrightarrow & 25x& = &-31 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-31}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-31}{25} & & \\ & V = \left\{ \frac{-31}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x+4)& = & -15 \color{red}{-} (-3+x) \\\Leftrightarrow & 24x+24& = &-15+3-x \\\Leftrightarrow & 24x \color{red}{+24} & = &-12 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 24x+x& = &-12-24 \\\Leftrightarrow & 25x& = &-36 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-36}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-36}{25} & & \\ & V = \left\{ \frac{-36}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x-4)& = & 9 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x-24& = &9+14-x \\\Leftrightarrow & 30x \color{red}{-24} & = &23 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 30x+x& = &23+24 \\\Leftrightarrow & 31x& = &47 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{47}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{47}{31} & & \\ & V = \left\{ \frac{47}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x-2)& = & 14 \color{red}{-} (-5+x) \\\Leftrightarrow & -12x-6& = &14+5-x \\\Leftrightarrow & -12x \color{red}{-6} & = &19 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &19+6 \\\Leftrightarrow & -11x& = &25 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{25}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-25}{11} & & \\ & V = \left\{ \frac{-25}{11} \right\} & \\\end{align}\)