Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{6})& = & -9x+\frac{4}{7} \\\Leftrightarrow & 20x-\frac{25}{6}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{840}{ \color{blue}{42} }x- \frac{175}{ \color{blue}{42} })& = & (\frac{-378}{ \color{blue}{42} }x+ \frac{24}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 840x \color{red}{-175} & = & \color{red}{-378x} +24 \\\Leftrightarrow & 840x \color{red}{-175} \color{blue}{+175} \color{blue}{+378x} & = & \color{red}{-378x} +24 \color{blue}{+378x} \color{blue}{+175} \\\Leftrightarrow & 840x+378x& = & 24+175 \\\Leftrightarrow & \color{red}{1218} x& = & 199 \\\Leftrightarrow & x = \frac{199}{1218} & & \\ & V = \left\{ \frac{199}{1218} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{9})& = & -8x+\frac{9}{7} \\\Leftrightarrow & -21x-\frac{28}{9}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1323}{ \color{blue}{63} }x- \frac{196}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1323x \color{red}{-196} & = & \color{red}{-504x} +81 \\\Leftrightarrow & -1323x \color{red}{-196} \color{blue}{+196} \color{blue}{+504x} & = & \color{red}{-504x} +81 \color{blue}{+504x} \color{blue}{+196} \\\Leftrightarrow & -1323x+504x& = & 81+196 \\\Leftrightarrow & \color{red}{-819} x& = & 277 \\\Leftrightarrow & x = \frac{277}{-819} & & \\\Leftrightarrow & x = \frac{-277}{819} & & \\ & V = \left\{ \frac{-277}{819} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{4}{11})& = & -5x+\frac{5}{3} \\\Leftrightarrow & -12x+\frac{24}{11}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+72} & = & \color{red}{-165x} +55 \\\Leftrightarrow & -396x \color{red}{+72} \color{blue}{-72} \color{blue}{+165x} & = & \color{red}{-165x} +55 \color{blue}{+165x} \color{blue}{-72} \\\Leftrightarrow & -396x+165x& = & 55-72 \\\Leftrightarrow & \color{red}{-231} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-231} & & \\\Leftrightarrow & x = \frac{17}{231} & & \\ & V = \left\{ \frac{17}{231} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{-147x} +56 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & -126x+147x& = & 56+18 \\\Leftrightarrow & \color{red}{21} x& = & 74 \\\Leftrightarrow & x = \frac{74}{21} & & \\ & V = \left\{ \frac{74}{21} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{9})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+56} & = & \color{red}{315x} +18 \\\Leftrightarrow & 504x \color{red}{+56} \color{blue}{-56} \color{blue}{-315x} & = & \color{red}{315x} +18 \color{blue}{-315x} \color{blue}{-56} \\\Leftrightarrow & 504x-315x& = & 18-56 \\\Leftrightarrow & \color{red}{189} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{189} & & \\ & V = \left\{ \frac{-38}{189} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{8})& = & 4x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{9}{8}& = & 4x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-360}{ \color{blue}{24} }x- \frac{27}{ \color{blue}{24} })& = & (\frac{96}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -360x \color{red}{-27} & = & \color{red}{96x} +16 \\\Leftrightarrow & -360x \color{red}{-27} \color{blue}{+27} \color{blue}{-96x} & = & \color{red}{96x} +16 \color{blue}{-96x} \color{blue}{+27} \\\Leftrightarrow & -360x-96x& = & 16+27 \\\Leftrightarrow & \color{red}{-456} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-456} & & \\\Leftrightarrow & x = \frac{-43}{456} & & \\ & V = \left\{ \frac{-43}{456} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{10})& = & 3x+\frac{8}{9} \\\Leftrightarrow & 35x-\frac{21}{10}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{3150}{ \color{blue}{90} }x- \frac{189}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 3150x \color{red}{-189} & = & \color{red}{270x} +80 \\\Leftrightarrow & 3150x \color{red}{-189} \color{blue}{+189} \color{blue}{-270x} & = & \color{red}{270x} +80 \color{blue}{-270x} \color{blue}{+189} \\\Leftrightarrow & 3150x-270x& = & 80+189 \\\Leftrightarrow & \color{red}{2880} x& = & 269 \\\Leftrightarrow & x = \frac{269}{2880} & & \\ & V = \left\{ \frac{269}{2880} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 8x+\frac{9}{2} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{112}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{-12} & = & \color{red}{112x} +63 \\\Leftrightarrow & 210x \color{red}{-12} \color{blue}{+12} \color{blue}{-112x} & = & \color{red}{112x} +63 \color{blue}{-112x} \color{blue}{+12} \\\Leftrightarrow & 210x-112x& = & 63+12 \\\Leftrightarrow & \color{red}{98} x& = & 75 \\\Leftrightarrow & x = \frac{75}{98} & & \\ & V = \left\{ \frac{75}{98} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-40} & = & \color{red}{315x} +54 \\\Leftrightarrow & -450x \color{red}{-40} \color{blue}{+40} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{+40} \\\Leftrightarrow & -450x-315x& = & 54+40 \\\Leftrightarrow & \color{red}{-765} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-765} & & \\\Leftrightarrow & x = \frac{-94}{765} & & \\ & V = \left\{ \frac{-94}{765} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{4}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -14x-\frac{28}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x- \frac{84}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{-84} & = & \color{red}{75x} +50 \\\Leftrightarrow & -210x \color{red}{-84} \color{blue}{+84} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+84} \\\Leftrightarrow & -210x-75x& = & 50+84 \\\Leftrightarrow & \color{red}{-285} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-285} & & \\\Leftrightarrow & x = \frac{-134}{285} & & \\ & V = \left\{ \frac{-134}{285} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & -4x+\frac{10}{9} \\\Leftrightarrow & 15x-\frac{20}{3}& = & -4x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{135}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{-36}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 135x \color{red}{-60} & = & \color{red}{-36x} +10 \\\Leftrightarrow & 135x \color{red}{-60} \color{blue}{+60} \color{blue}{+36x} & = & \color{red}{-36x} +10 \color{blue}{+36x} \color{blue}{+60} \\\Leftrightarrow & 135x+36x& = & 10+60 \\\Leftrightarrow & \color{red}{171} x& = & 70 \\\Leftrightarrow & x = \frac{70}{171} & & \\ & V = \left\{ \frac{70}{171} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{7})& = & 7x+\frac{9}{5} \\\Leftrightarrow & -30x-\frac{24}{7}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{120}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-120} & = & \color{red}{245x} +63 \\\Leftrightarrow & -1050x \color{red}{-120} \color{blue}{+120} \color{blue}{-245x} & = & \color{red}{245x} +63 \color{blue}{-245x} \color{blue}{+120} \\\Leftrightarrow & -1050x-245x& = & 63+120 \\\Leftrightarrow & \color{red}{-1295} x& = & 183 \\\Leftrightarrow & x = \frac{183}{-1295} & & \\\Leftrightarrow & x = \frac{-183}{1295} & & \\ & V = \left\{ \frac{-183}{1295} \right\} & \\\end{align}\)