Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & -8x+\frac{8}{5} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{-70} & = & \color{red}{-120x} +24 \\\Leftrightarrow & -315x \color{red}{-70} \color{blue}{+70} \color{blue}{+120x} & = & \color{red}{-120x} +24 \color{blue}{+120x} \color{blue}{+70} \\\Leftrightarrow & -315x+120x& = & 24+70 \\\Leftrightarrow & \color{red}{-195} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-195} & & \\\Leftrightarrow & x = \frac{-94}{195} & & \\ & V = \left\{ \frac{-94}{195} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -14x-\frac{21}{8}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-112}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -112x \color{red}{-21} & = & \color{red}{24x} +36 \\\Leftrightarrow & -112x \color{red}{-21} \color{blue}{+21} \color{blue}{-24x} & = & \color{red}{24x} +36 \color{blue}{-24x} \color{blue}{+21} \\\Leftrightarrow & -112x-24x& = & 36+21 \\\Leftrightarrow & \color{red}{-136} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-136} & & \\\Leftrightarrow & x = \frac{-57}{136} & & \\ & V = \left\{ \frac{-57}{136} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{3})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 8x+\frac{10}{3}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{+10} & = & \color{red}{-21x} +8 \\\Leftrightarrow & 24x \color{red}{+10} \color{blue}{-10} \color{blue}{+21x} & = & \color{red}{-21x} +8 \color{blue}{+21x} \color{blue}{-10} \\\Leftrightarrow & 24x+21x& = & 8-10 \\\Leftrightarrow & \color{red}{45} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{45} & & \\ & V = \left\{ \frac{-2}{45} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{+54} & = & \color{red}{231x} +110 \\\Leftrightarrow & -990x \color{red}{+54} \color{blue}{-54} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{-54} \\\Leftrightarrow & -990x-231x& = & 110-54 \\\Leftrightarrow & \color{red}{-1221} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-1221} & & \\\Leftrightarrow & x = \frac{-56}{1221} & & \\ & V = \left\{ \frac{-56}{1221} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & -4x+\frac{4}{3} \\\Leftrightarrow & -35x-\frac{21}{8}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-96}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-63} & = & \color{red}{-96x} +32 \\\Leftrightarrow & -840x \color{red}{-63} \color{blue}{+63} \color{blue}{+96x} & = & \color{red}{-96x} +32 \color{blue}{+96x} \color{blue}{+63} \\\Leftrightarrow & -840x+96x& = & 32+63 \\\Leftrightarrow & \color{red}{-744} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-744} & & \\\Leftrightarrow & x = \frac{-95}{744} & & \\ & V = \left\{ \frac{-95}{744} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{9})& = & 4x+\frac{7}{2} \\\Leftrightarrow & -28x+\frac{28}{9}& = & 4x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-504}{ \color{blue}{18} }x+ \frac{56}{ \color{blue}{18} })& = & (\frac{72}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -504x \color{red}{+56} & = & \color{red}{72x} +63 \\\Leftrightarrow & -504x \color{red}{+56} \color{blue}{-56} \color{blue}{-72x} & = & \color{red}{72x} +63 \color{blue}{-72x} \color{blue}{-56} \\\Leftrightarrow & -504x-72x& = & 63-56 \\\Leftrightarrow & \color{red}{-576} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-576} & & \\\Leftrightarrow & x = \frac{-7}{576} & & \\ & V = \left\{ \frac{-7}{576} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{3})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{+8} & = & \color{red}{27x} +8 \\\Leftrightarrow & -24x \color{red}{+8} \color{blue}{-8} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{-8} \\\Leftrightarrow & -24x-27x& = & 8-8 \\\Leftrightarrow & \color{red}{-51} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-51} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{3})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{10}{3}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+70} & = & \color{red}{105x} +12 \\\Leftrightarrow & 126x \color{red}{+70} \color{blue}{-70} \color{blue}{-105x} & = & \color{red}{105x} +12 \color{blue}{-105x} \color{blue}{-70} \\\Leftrightarrow & 126x-105x& = & 12-70 \\\Leftrightarrow & \color{red}{21} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{21} & & \\ & V = \left\{ \frac{-58}{21} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{3}{8})& = & -9x+\frac{8}{9} \\\Leftrightarrow & 28x+\frac{21}{8}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2016}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{-648}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2016x \color{red}{+189} & = & \color{red}{-648x} +64 \\\Leftrightarrow & 2016x \color{red}{+189} \color{blue}{-189} \color{blue}{+648x} & = & \color{red}{-648x} +64 \color{blue}{+648x} \color{blue}{-189} \\\Leftrightarrow & 2016x+648x& = & 64-189 \\\Leftrightarrow & \color{red}{2664} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{2664} & & \\ & V = \left\{ \frac{-125}{2664} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{7})& = & 4x+\frac{4}{5} \\\Leftrightarrow & -15x+\frac{20}{7}& = & 4x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+100} & = & \color{red}{140x} +28 \\\Leftrightarrow & -525x \color{red}{+100} \color{blue}{-100} \color{blue}{-140x} & = & \color{red}{140x} +28 \color{blue}{-140x} \color{blue}{-100} \\\Leftrightarrow & -525x-140x& = & 28-100 \\\Leftrightarrow & \color{red}{-665} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{-665} & & \\\Leftrightarrow & x = \frac{72}{665} & & \\ & V = \left\{ \frac{72}{665} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{3})& = & -6x+\frac{10}{3} \\\Leftrightarrow & -35x-\frac{14}{3}& = & -6x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-18}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{-14} & = & \color{red}{-18x} +10 \\\Leftrightarrow & -105x \color{red}{-14} \color{blue}{+14} \color{blue}{+18x} & = & \color{red}{-18x} +10 \color{blue}{+18x} \color{blue}{+14} \\\Leftrightarrow & -105x+18x& = & 10+14 \\\Leftrightarrow & \color{red}{-87} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-87} & & \\\Leftrightarrow & x = \frac{-8}{29} & & \\ & V = \left\{ \frac{-8}{29} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{16}{7}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+80} & = & \color{red}{105x} +42 \\\Leftrightarrow & -280x \color{red}{+80} \color{blue}{-80} \color{blue}{-105x} & = & \color{red}{105x} +42 \color{blue}{-105x} \color{blue}{-80} \\\Leftrightarrow & -280x-105x& = & 42-80 \\\Leftrightarrow & \color{red}{-385} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-385} & & \\\Leftrightarrow & x = \frac{38}{385} & & \\ & V = \left\{ \frac{38}{385} \right\} & \\\end{align}\)