Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{5})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{12}{5}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+84} & = & \color{red}{-105x} +10 \\\Leftrightarrow & 280x \color{red}{+84} \color{blue}{-84} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{-84} \\\Leftrightarrow & 280x+105x& = & 10-84 \\\Leftrightarrow & \color{red}{385} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{385} & & \\ & V = \left\{ \frac{-74}{385} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{3})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 20x+\frac{10}{3}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+110} & = & \color{red}{-99x} +24 \\\Leftrightarrow & 660x \color{red}{+110} \color{blue}{-110} \color{blue}{+99x} & = & \color{red}{-99x} +24 \color{blue}{+99x} \color{blue}{-110} \\\Leftrightarrow & 660x+99x& = & 24-110 \\\Leftrightarrow & \color{red}{759} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{759} & & \\ & V = \left\{ \frac{-86}{759} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-24} & = & \color{red}{25x} +4 \\\Leftrightarrow & 60x \color{red}{-24} \color{blue}{+24} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{+24} \\\Leftrightarrow & 60x-25x& = & 4+24 \\\Leftrightarrow & \color{red}{35} x& = & 28 \\\Leftrightarrow & x = \frac{28}{35} & & \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & 5x+\frac{7}{3} \\\Leftrightarrow & -4x-\frac{10}{7}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{-30} & = & \color{red}{105x} +49 \\\Leftrightarrow & -84x \color{red}{-30} \color{blue}{+30} \color{blue}{-105x} & = & \color{red}{105x} +49 \color{blue}{-105x} \color{blue}{+30} \\\Leftrightarrow & -84x-105x& = & 49+30 \\\Leftrightarrow & \color{red}{-189} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-189} & & \\\Leftrightarrow & x = \frac{-79}{189} & & \\ & V = \left\{ \frac{-79}{189} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{3})& = & 9x+\frac{7}{5} \\\Leftrightarrow & -4x+\frac{4}{3}& = & 9x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+20} & = & \color{red}{135x} +21 \\\Leftrightarrow & -60x \color{red}{+20} \color{blue}{-20} \color{blue}{-135x} & = & \color{red}{135x} +21 \color{blue}{-135x} \color{blue}{-20} \\\Leftrightarrow & -60x-135x& = & 21-20 \\\Leftrightarrow & \color{red}{-195} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-195} & & \\\Leftrightarrow & x = \frac{-1}{195} & & \\ & V = \left\{ \frac{-1}{195} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{3})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{20}{3}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-140} & = & \color{red}{147x} +27 \\\Leftrightarrow & -210x \color{red}{-140} \color{blue}{+140} \color{blue}{-147x} & = & \color{red}{147x} +27 \color{blue}{-147x} \color{blue}{+140} \\\Leftrightarrow & -210x-147x& = & 27+140 \\\Leftrightarrow & \color{red}{-357} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-357} & & \\\Leftrightarrow & x = \frac{-167}{357} & & \\ & V = \left\{ \frac{-167}{357} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & 9x+\frac{5}{4} \\\Leftrightarrow & 28x+\frac{14}{3}& = & 9x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{336}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 336x \color{red}{+56} & = & \color{red}{108x} +15 \\\Leftrightarrow & 336x \color{red}{+56} \color{blue}{-56} \color{blue}{-108x} & = & \color{red}{108x} +15 \color{blue}{-108x} \color{blue}{-56} \\\Leftrightarrow & 336x-108x& = & 15-56 \\\Leftrightarrow & \color{red}{228} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{228} & & \\ & V = \left\{ \frac{-41}{228} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{11})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -20x+\frac{25}{11}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{175}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+175} & = & \color{red}{539x} +44 \\\Leftrightarrow & -1540x \color{red}{+175} \color{blue}{-175} \color{blue}{-539x} & = & \color{red}{539x} +44 \color{blue}{-539x} \color{blue}{-175} \\\Leftrightarrow & -1540x-539x& = & 44-175 \\\Leftrightarrow & \color{red}{-2079} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{-2079} & & \\\Leftrightarrow & x = \frac{131}{2079} & & \\ & V = \left\{ \frac{131}{2079} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{3})& = & 9x+\frac{4}{3} \\\Leftrightarrow & 14x-\frac{14}{3}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{-14} & = & \color{red}{27x} +4 \\\Leftrightarrow & 42x \color{red}{-14} \color{blue}{+14} \color{blue}{-27x} & = & \color{red}{27x} +4 \color{blue}{-27x} \color{blue}{+14} \\\Leftrightarrow & 42x-27x& = & 4+14 \\\Leftrightarrow & \color{red}{15} x& = & 18 \\\Leftrightarrow & x = \frac{18}{15} & & \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{18}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+54} & = & \color{red}{75x} +10 \\\Leftrightarrow & -180x \color{red}{+54} \color{blue}{-54} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-54} \\\Leftrightarrow & -180x-75x& = & 10-54 \\\Leftrightarrow & \color{red}{-255} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-255} & & \\\Leftrightarrow & x = \frac{44}{255} & & \\ & V = \left\{ \frac{44}{255} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{528}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 528x \color{red}{+36} & = & \color{red}{154x} +55 \\\Leftrightarrow & 528x \color{red}{+36} \color{blue}{-36} \color{blue}{-154x} & = & \color{red}{154x} +55 \color{blue}{-154x} \color{blue}{-36} \\\Leftrightarrow & 528x-154x& = & 55-36 \\\Leftrightarrow & \color{red}{374} x& = & 19 \\\Leftrightarrow & x = \frac{19}{374} & & \\ & V = \left\{ \frac{19}{374} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{7})& = & 5x+\frac{8}{7} \\\Leftrightarrow & -12x+\frac{18}{7}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x+ \frac{18}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{+18} & = & \color{red}{35x} +8 \\\Leftrightarrow & -84x \color{red}{+18} \color{blue}{-18} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{-18} \\\Leftrightarrow & -84x-35x& = & 8-18 \\\Leftrightarrow & \color{red}{-119} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-119} & & \\\Leftrightarrow & x = \frac{10}{119} & & \\ & V = \left\{ \frac{10}{119} \right\} & \\\end{align}\)